統計場論與量子相變

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.

Solid state physics I, II, Advanced Solid State Physics I,II Quantum Mechanics I,II

無備註

TA available to grade HWs, provide solutions on the NCTU-e3 website. link to the class-time discussion: https://meet.google.com/avk-qpnh-snf

作業部份: There will be homework every week. 考試部份: No mid-term exam. There will be a final take-home exam. 評量部份: 70% Homework 30% Final exam

• Introduction to phase transitions

  Scaling and power-laws in statistical physics

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  2

• How phase transitions occur in principle I

  *Review of statistical mechanics *The thermodynamic limit *Phase boundaries and phase transitions

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  2

• How phase transitions occur in principle II

  *The Ising model * existence of phase transition *Spontaneous symmetry breaking

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  2

• *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

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  4

• Landau-Ginsburg theory of phase transitions

  *Order parameters *first-order and continuous phase transitions *Correlation functions

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  2

• Fluctuations and the breakdown of the Landau theory

  *Breakdown of microscopic and phenomenological Landau theory *The Gaussian approximation *Critical exponents

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  3

• Scaling hypothesis and relations

  *The static scaling hypothesis *Other forms of scaling hypothesis

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  2

• 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

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  6

• Continuous symmetry and Kosterlitz-Thouless transition

  *Correlation in the ordered phase *Kosterlitz-Thouless transition

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  3

• Critical phenomena near four dimensions

  *Epsilon-expansion approach *RG for Gaussian model *RG beyond Gaussian model *Feynman diagram and RG recursion relations

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  4

• Introduction to quantum phase transitions

  *Zero temperature phase transition *Finite temperature crossover *Quantum classical mapping *Difference between classical and quantum phase transitions

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  4

• 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

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  6

• 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

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  6

• *Physics close to upper critical dimension

  *Field theoretical RG approach to quantum rotor model

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  3

1.Lectures on phase transitions and the renormalization group, Nigel Goldenfeld, Addison Wesley 1992 2.Quantum phase transitions, Subir Sachdev, Cambridge University, 2011.

地點

SC453

時間

Office hours: Mon. 2:00pm-3:00pm Wed. 2:00pm-3:00pm Fri. 2:00pm-3:00pm

聯絡方式

chung@nctu.edu.tw Tel: 03-5712121#56107