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  

WeekCourse ContentCourse VideoCourse Download
Course Introduction
Ch1.1 Scaling & dimensional analysis
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Ch1.2 Power laws in statistical physicsWatch OnlineMP4 Download
Ch2.1&Ch2.2 Phase transition in principle —Universality &Scaling lawsWatch OnlineMP4 Download
Ch2.2 & Ch2.3 Thermaldynamic Limit & Phase boundaryWatch OnlineMP4 Download
Ch2.3 Type of phase transition & Finite size effect
Ch2.5 Ising model
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Ch2.5 Ising modelWatch OnlineMP4 Download
Ch2.7 Symmetry property of Ising magnetWatch OnlineMP4 Download
Ch2.8 Ising Ferromagnet & domain wallWatch OnlineMP4 Download
Ch2.9 Spontaneous symmetry brokenWatch OnlineMP4 Download
Ch2.10 (I) Ergodicity breaking
Ch2.11~Ch2.12 (II) Link from fluid to Ising model
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Ch2.11~CH2.13 Mapping from continuous fluid to Ising modelWatch OnlineMP4 Download
Ch2.11~Ch2.13 Conclusion of continuous fluid to Ising model
Ch3.1 AD HOC solution methods
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Ch3.2 Transfer matrix
Ch3.3 Perron's theorem
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Ch3.4 Thermaldynamic propertiesWatch OnlineMP4 Download
Ch3.5 Spatial correlationsWatch OnlineMP4 Download
Ch3.5~Ch3.7 Two spins correlations function & solvable Ising modelWatch OnlineMP4 Download
Ch3.7 Ising model mean field theoryWatch OnlineMP4 Download
Ch3.7 D-dimensions Ising model mean field theoryWatch OnlineMP4 Download
Ch 5.3 Landau theoryWatch OnlineMP4 Download
CH5.5 Landau theory & First order transitionWatch OnlineMP4 Download
Ch5.6 Landau’s free energyWatch OnlineMP4 Download
Ch5.7 Landau’s free energy Green’s functionWatch OnlineMP4 Download
Ch6.1& Ch6.2 Breakdown Landau theoryWatch OnlineMP4 Download
Ch6.2 Breakdown Landau theory
Ch6.3 Gaussian Approximation
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Ch6.3 Gaussian ApproximationWatch OnlineMP4 Download
Ch7.1 Anomalous DimensionsWatch OnlineMP4 Download
Ch7.2 Dimensional analysis
Ch8.1 Scaling
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Ch8.2 Scaling hypothesis
Ch9.1 block spin
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Ch9.1 Kadanoff’s block spin
Ch9.2 Renormalization group
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Ch9.2 Renormalization groupWatch OnlineMP4 Download
Ch9.3 Renormalization group—fixed pointsWatch OnlineMP4 Download
Ch9.4 Renormalization group transformationWatch OnlineMP4 Download
Ch9.6 RG for the two dimensional Ising modelWatch OnlineMP4 Download

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%
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