{"id":106575,"date":"2023-11-11T15:14:21","date_gmt":"2023-11-11T07:14:21","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=106575"},"modified":"2024-11-18T13:35:04","modified_gmt":"2024-11-18T05:35:04","slug":"statistical-field-theory-and-quantum-phase-transitions-110-academic-year-department-of-electrophysics-prof-chung-hou-chung","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-electrophysics\/statistical-field-theory-and-quantum-phase-transitions-110-academic-year-department-of-electrophysics-prof-chung-hou-chung","title":{"rendered":"Statistical Field Theory and Quantum Phase Transitions &#8211; 110 Academic Year | Department of Electrophysics Prof. Chung-Hou Chung"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"106575\" class=\"elementor elementor-106575\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky 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class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">Statistical Field Theory and Quantum Phase Transitions - 110 Academic Year<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-home\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M280.37 148.26L96 300.11V464a16 16 0 0 0 16 16l112.06-.29a16 16 0 0 0 15.92-16V368a16 16 0 0 1 16-16h64a16 16 0 0 1 16 16v95.64a16 16 0 0 0 16 16.05L464 480a16 16 0 0 0 16-16V300L295.67 148.26a12.19 12.19 0 0 0-15.3 0zM571.6 251.47L488 182.56V44.05a12 12 0 0 0-12-12h-56a12 12 0 0 0-12 12v72.61L318.47 43a48 48 0 0 0-61 0L4.34 251.47a12 12 0 0 0-1.6 16.9l25.5 31A12 12 0 0 0 45.15 301l235.22-193.74a12.19 12.19 0 0 1 15.3 0L530.9 301a12 12 0 0 0 16.9-1.6l25.5-31a12 12 0 0 0-1.7-16.93z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Homepage<\/span>                            \n                                                    <\/li>\n                                            <li id=\"video\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"2\" role=\"tab\" tabindex=\"-1\" aria-controls=\"video-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-video\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336.2 64H47.8C21.4 64 0 85.4 0 111.8v288.4C0 426.6 21.4 448 47.8 448h288.4c26.4 0 47.8-21.4 47.8-47.8V111.8c0-26.4-21.4-47.8-47.8-47.8zm189.4 37.7L416 177.3v157.4l109.6 75.5c21.2 14.6 50.4-.3 50.4-25.8V127.5c0-25.4-29.1-40.4-50.4-25.8z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Video<\/span>                            \n                                                    <\/li>\n                                            <li id=\"syllabus\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"3\" role=\"tab\" tabindex=\"-1\" aria-controls=\"syllabus-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 48-21.5 48-48V112c0-26.5-21.5-48-48-48zM96 424c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm96-192c13.3 0 24 10.7 24 24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Syllabus<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/ep.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u96fb\u5b50\u7269\u7406\u7cfb<\/a>\u63d0\u4f9b\u3002<\/p><p class=\"text\">Phase transitions are broad and generic phenomenon in many-body systems where the state of matter transforms from one to the other with the change of external parameters.<\/p><p>\u00a0<\/p><p class=\"text\">This course is the introduction to phase transitions in statistical mechanics. The classical phase transitions are driven by thermal fluctuations, while the quantum phase transitions are driven by quantum fluctuations.<\/p><p>\u00a0<\/p><p class=\"text\">Near the transitions, physical observables show universal power-law scaling. Critical phenomena in various physical systems are discussed. Statistical field theory based on Landau-Ginsburg theory is used to describe these phase transitions. The goal of this course is to give students a modern introductory understanding in classical and quantum phase transitions as well as critical phenomenon via field theory approach.<\/p><p>\u00a0<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><\/p><p class=\"text\">Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992<\/p><p class=\"text\">Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.<\/p><p><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<\/span><\/p><p>\u00a0<\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">Instructor(s)<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Department of Electrophysics Prof. Chung-Hou Chung<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u00a0Credits<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0110 Academic Year<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Graduate Student<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Solid state physics I, II, Advanced Solid State Physics I,II Quantum Mechanics I,II<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0<a href=\"#syllabus\">Course Syllabus<\/a>\u00a0\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-502\" class=\"tablepress tablepress-id-502\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Course Introduction<br \/>\nCh1.1 Scaling &amp; dimensional analysis<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=106590\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch1.2 Power laws in statistical physics<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108300\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.1&amp;Ch2.2 Phase transition in principle \u2014Universality &amp;Scaling laws<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108306\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.2 &amp; Ch2.3 Thermaldynamic Limit &amp; Phase boundary<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108312\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.3 Type of phase transition &amp; Finite size effect<br \/>\nCh2.5 Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108318\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.5 Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108324\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.7 Symmetry property of Ising magnet<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108348\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.8 Ising Ferromagnet &amp; domain wall<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108354\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.9 Spontaneous symmetry broken<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108362\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.10 (I) Ergodicity breaking<br \/>\nCh2.11~Ch2.12 (II) Link from fluid to Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108368\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.11~CH2.13 Mapping from continuous fluid to Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108374\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch2.11~Ch2.13 Conclusion of continuous fluid to Ising model<br \/>\nCh3.1 AD HOC solution methods<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108380\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.2 Transfer matrix<br \/>\nCh3.3 Perron's theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108386\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.4 Thermaldynamic properties<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108392\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.5 Spatial correlations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108400\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.5~Ch3.7 Two spins correlations function &amp; solvable Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108406\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.7 Ising model mean field theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108412\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch3.7 D-dimensions Ising model mean field theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108418\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch 5.3 Landau theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108424\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH5.5 Landau theory &amp; First order transition<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108430\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch5.6 Landau\u2019s free energy<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108436\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch5.7 Landau\u2019s free energy Green\u2019s function<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108442\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch6.1&amp; Ch6.2 Breakdown Landau theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108448\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch6.2 Breakdown Landau theory<br \/>\nCh6.3 Gaussian Approximation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108454\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch6.3 Gaussian Approximation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108460\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch7.1 Anomalous Dimensions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108468\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch7.2 Dimensional analysis<br \/>\nCh8.1 Scaling<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108474\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch8.2 Scaling hypothesis<br \/>\nCh9.1 block spin<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108480\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch9.1 Kadanoff\u2019s block spin<br \/>\nCh9.2 Renormalization group<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108486\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch9.2 Renormalization group<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108492\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch9.3 Renormalization group\u2014fixed points<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108498\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch9.4 Renormalization group transformation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108504\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Ch9.6 RG for the two dimensional Ising model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=108510\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-502 from cache -->\u00a0<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">Phase transitions are broad and generic phenomenon in many-body systems where the state of matter transforms from one to the other with the change of external parameters. This course is the introduction to phase transitions in statistical mechanics. The classical phase transitions are driven by thermal fluctuations, while the quantum phase transitions are driven by quantum fluctuations. Near the transitions, physical observables show universal power-law scaling. Critical phenomena in various physical systems are discussed. Statistical field theory based on Landau-Ginsburg theory is used to describe these phase transitions. The goal of this course is to give students a modern introductory understanding in classical and quantum phase transitions as well as critical phenomenon via field theory approach.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Introduction to phase transitions<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Scaling and power-laws in statistical physics <\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">How phase transitions occur in principle I<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Review of statistical mechanics<\/p><p class=\"text\">*The thermodynamic limit<\/p><p class=\"text\">*Phase boundaries and phase transitions<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">How phase transitions occur in principle II<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*The Ising model<\/p><p class=\"text\">* existence of phase transition<\/p><p class=\"text\">*Spontaneous symmetry breaking<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">*How phase transitions occur in practice (Ising model)<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Ad Hoc solution methods<\/p><p class=\"text\">*The transfer matrix<\/p><p class=\"text\">*Phase transition of Ising model *Thermodynamic properties<\/p><p class=\"text\">*Spatial correlations<\/p><p class=\"text\">*Low temperature expansion<\/p><p class=\"text\">*Mean field theory<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Landau-Ginsburg theory of phase transitions<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*Order parameters<\/p><p class=\"text\">*first-order and continuous phase transitions<\/p><p class=\"text\">*Correlation functions<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Fluctuations and the breakdown of the Landau theory<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Breakdown of microscopic and phenomenological Landau theory<\/p><p class=\"text\">*The Gaussian approximation<\/p><p class=\"text\">*Critical exponents<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Scaling hypothesis and relations<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*The static scaling hypothesis<\/p><p class=\"text\">*Other forms of scaling hypothesis<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">The renormalization group (RG)<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Block spins<\/p><p class=\"text\">*Basic ideas of RG<\/p><p class=\"text\">*Fixed points<\/p><p class=\"text\">*Origin of scaling<\/p><p class=\"text\">*RG for 2D Ising model<\/p><p class=\"text\">*RG for correlation functions<\/p><p class=\"text\">*Crossover phenomena<\/p><p class=\"text\">*Correction to scaling and finite-size scaling<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Continuous symmetry and Kosterlitz-Thouless transition<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*Correlation in the ordered phase<\/p><p class=\"text\">*Kosterlitz-Thouless transition<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Critical phenomena near four dimensions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Epsilon-expansion approach<\/p><p class=\"text\">*RG for Gaussian model<\/p><p class=\"text\">*RG beyond Gaussian model<\/p><p class=\"text\">*Feynman diagram and RG recursion relations<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Introduction to quantum phase transitions<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*Zero temperature phase transition<\/p><p class=\"text\">*Finite temperature crossover<\/p><p class=\"text\">*Quantum classical mapping<\/p><p class=\"text\">*Difference between classical and quantum phase transitions<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Quantum rotor model at T=0<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><p class=\"text\">*Global phase diagram<\/p><p class=\"text\">*Mapping to classical field theory<\/p><p class=\"text\">*Spectrum of quantum field theory<\/p><p class=\"text\">*Correlations, susceptibilities at quantum critical point<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Quantum rotor model at finite temperatures<\/span><\/td><td style=\"padding: 5px;\"><p class=\"text\">*Low T on quantum paramagnetic side<\/p><p class=\"text\">*Low T on the magnetically ordered side<\/p><p class=\"text\">*High T in quantum critical region<\/p><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">*Physics close to upper critical dimension<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">*Field theoretical RG approach to quantum rotor model <\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">1. Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992<\/p><p class=\"text\">2. Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Homework<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">70%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Final exam<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">30%<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d7723a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d7723a8\" 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Statistical Fi&hellip;<\/p>\n","protected":false},"featured_media":106566,"parent":5290,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","format":"standard","meta":{"footnotes":""},"categories":[248],"tags":[341,345,2790,9029],"class_list":["post-106575","course_page","type-course_page","status-publish","format-standard","has-post-thumbnail","hentry","category-department-of-electrophysics-en","tag-label-all-course-en","tag-label-college-of-science-en","tag-label-electrophysics-en","tag-label-statistical-field-theory-and-quantum-phase-transitions-110-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Statistical Field Theory and Quantum 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