Statistical Field Theory and Quantum Phase Transitions - 110 Academic Year
本課程是由 國立陽明交通大學電子物理系提供。
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.
Textbook：
Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992
Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.
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| Instructor(s) | Department of Electrophysics Prof. Chung-Hou Chung |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 110 Academic Year |
| Level | Graduate Student |
| Prior Knowledge | Solid state physics I, II, Advanced Solid State Physics I,II Quantum Mechanics I,II |
| Related Resources | Course Video Course Syllabus |
| Week | Course Content | Course Video |
|---|---|---|
| Course Introduction Ch1.1 Scaling & dimensional analysis | Watch Online | |
| Ch1.2 Power laws in statistical physics | Watch Online | |
| Ch2.1&Ch2.2 Phase transition in principle —Universality &Scaling laws | Watch Online | |
| Ch2.2 & Ch2.3 Thermaldynamic Limit & Phase boundary | Watch Online | |
| Ch2.3 Type of phase transition & Finite size effect Ch2.5 Ising model | Watch Online | |
| Ch2.5 Ising model | Watch Online | |
| Ch2.7 Symmetry property of Ising magnet | Watch Online | |
| Ch2.8 Ising Ferromagnet & domain wall | Watch Online | |
| Ch2.9 Spontaneous symmetry broken | Watch Online | |
| Ch2.10 (I) Ergodicity breaking Ch2.11~Ch2.12 (II) Link from fluid to Ising model | Watch Online | |
| Ch2.11~CH2.13 Mapping from continuous fluid to Ising model | Watch Online | |
| Ch2.11~Ch2.13 Conclusion of continuous fluid to Ising model Ch3.1 AD HOC solution methods | Watch Online | |
| Ch3.2 Transfer matrix Ch3.3 Perron's theorem | Watch Online | |
| Ch3.4 Thermaldynamic properties | Watch Online | |
| Ch3.5 Spatial correlations | Watch Online | |
| Ch3.5~Ch3.7 Two spins correlations function & solvable Ising model | Watch Online | |
| Ch3.7 Ising model mean field theory | Watch Online | |
| Ch3.7 D-dimensions Ising model mean field theory | Watch Online | |
| Ch 5.3 Landau theory | Watch Online | |
| CH5.5 Landau theory & First order transition | Watch Online | |
| Ch5.6 Landau’s free energy | Watch Online | |
| Ch5.7 Landau’s free energy Green’s function | Watch Online | |
| Ch6.1& Ch6.2 Breakdown Landau theory | Watch Online | |
| Ch6.2 Breakdown Landau theory Ch6.3 Gaussian Approximation | Watch Online | |
| Ch6.3 Gaussian Approximation | Watch Online | |
| Ch7.1 Anomalous Dimensions | Watch Online | |
| Ch7.2 Dimensional analysis Ch8.1 Scaling | Watch Online | |
| Ch8.2 Scaling hypothesis Ch9.1 block spin | Watch Online | |
| Ch9.1 Kadanoff’s block spin Ch9.2 Renormalization group | Watch Online | |
| Ch9.2 Renormalization group | Watch Online | |
| Ch9.3 Renormalization group—fixed points | Watch Online | |
| Ch9.4 Renormalization group transformation | Watch Online | |
| Ch9.6 RG for the two dimensional Ising model | Watch Online |
課程目標
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.
課程章節
| 章節 | 章節內容 |
| Introduction to phase transitions | Scaling and power-laws in statistical physics |
| How phase transitions occur in principle I | *Review of statistical mechanics *The thermodynamic limit *Phase boundaries and phase transitions |
| How phase transitions occur in principle II | *The Ising model * existence of phase transition *Spontaneous symmetry breaking |
| *How phase transitions occur in practice (Ising model) | *Ad Hoc solution methods *The transfer matrix *Phase transition of Ising model *Thermodynamic properties *Spatial correlations *Low temperature expansion *Mean field theory |
| Landau-Ginsburg theory of phase transitions | *Order parameters *first-order and continuous phase transitions *Correlation functions |
| Fluctuations and the breakdown of the Landau theory | *Breakdown of microscopic and phenomenological Landau theory *The Gaussian approximation *Critical exponents |
| Scaling hypothesis and relations | *The static scaling hypothesis *Other forms of scaling hypothesis |
| The renormalization group (RG) | *Block spins *Basic ideas of RG *Fixed points *Origin of scaling *RG for 2D Ising model *RG for correlation functions *Crossover phenomena *Correction to scaling and finite-size scaling |
| Continuous symmetry and Kosterlitz-Thouless transition | *Correlation in the ordered phase *Kosterlitz-Thouless transition |
| Critical phenomena near four dimensions | *Epsilon-expansion approach *RG for Gaussian model *RG beyond Gaussian model *Feynman diagram and RG recursion relations |
| Introduction to quantum phase transitions | *Zero temperature phase transition *Finite temperature crossover *Quantum classical mapping *Difference between classical and quantum phase transitions |
| Quantum rotor model at T=0 | *Global phase diagram *Mapping to classical field theory *Spectrum of quantum field theory *Correlations, susceptibilities at quantum critical point |
| Quantum rotor model at finite temperatures | *Low T on quantum paramagnetic side *Low T on the magnetically ordered side *High T in quantum critical region |
| *Physics close to upper critical dimension | *Field theoretical RG approach to quantum rotor model |
課程書目
1. Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992
2. Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.
評分標準
| 項目 | 百分比 |
| Homework | 70% |
| Final exam | 30% |