Statistical Field Theory and Quantum Phase Transitions - 110 Academic Year

統計場論與量子相變 - 110學年度

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.

 

課程用書:

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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授課教師 電子物理系 仲崇厚老師
課程學分 3學分
授課年度 110學年度
授課對象 研究所
預備知識 Solid state physics I, II, Advanced Solid State Physics I,II Quantum Mechanics I,II
課程提供 課程影音   課程綱要  

週次課程內容課程影音課程下載
課程介紹
Ch1.1 分析尺度及量綱
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Ch1.2 統計物理學中的冪律線上觀看MP4下載
Ch2.1& Ch2.2 相變理論—普遍類及尺度理論線上觀看MP4下載
Ch2.2 & Ch2.3 熱⼒學極限 &相位邊界線上觀看MP4下載
Ch2.3 相變種類及有限尺度效應
Ch2.5 伊辛模型
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Ch2.5 伊辛模型線上觀看MP4下載
Ch2.7 伊辛模型對稱性質線上觀看MP4下載
Ch2.8 伊辛模型-鐵磁性線上觀看MP4下載
Ch2.9 ⾃發性對稱破壞線上觀看MP4下載
Ch2.10 (I)遍歷性破壞
Ch2.11~CH2.12 (II) 將流體連結到伊辛模型
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Ch2.11~CH2.13 從連續流體映射到伊辛模型線上觀看MP4下載
Ch2.11~Ch2.13 連續流體到伊辛模型的結論
Ch3.1 AD HOC 解決⽅法
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Ch3.2 傳輸矩陣
Ch3.3 Perron’s理論
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Ch3.4 熱動⼒學性質線上觀看MP4下載
Ch3.5 空間相關性線上觀看MP4下載
Ch3.5~Ch3.7 雙⾃旋關聯函數 & 解伊辛模型線上觀看MP4下載
Ch3.7 伊辛模型-平均場論線上觀看MP4下載
Ch3.7 D-維伊辛模型-平均場論線上觀看MP4下載
Ch 5.3朗道理論線上觀看MP4下載
CH5.5 朗道理論 & ⼀階相變線上觀看MP4下載
Ch5.6 朗道⾃由能線上觀看MP4下載
Ch5.7 朗道⾃由能格林函數線上觀看MP4下載
Ch6.1 & Ch6.2 朗道理論的崩壞線上觀看MP4下載
Ch6.2 朗道理論的崩壞
Ch6.3 ⾼斯近似
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Ch6.3 ⾼斯近似線上觀看MP4下載
CH7.1 奇異維度線上觀看MP4下載
Ch7.2 維度分析
Ch8.1 尺度分析
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Ch8.2 尺度假設
Ch9.1 塊⾃旋
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Ch9.1卡達諾夫塊⾃旋
Ch9.2 重整化群
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Ch9.2 重整化群線上觀看MP4下載
Ch9.3 重整化群—定點線上觀看MP4下載
Ch9.4 重整化群轉換線上觀看MP4下載
Ch9.6 ⼆維伊辛模型的重整化群線上觀看MP4下載

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 transitionsScaling 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
Homework70%
Final exam30%