Course curriculum

  • 1

    Course Overview

    • Course Overview

    • Study Text - Part 1

    • Study Text - Part 2
  • 2

    Lecture 1: Review of Thermodynamics - Thermodynamic Laws, Temperature, Energy, Heat, Entropy

    • 1.1 Basic Concepts

    • 1.2 Zeroth and First Laws

    • 1.3 Second Law

    • 1.4 Entropy

    • 1.5 Third Law and Thermodynamic Potential

    • Tutorial 1

    • Solutions 1
  • 3

    Lecture 2: Basics of Statistical Physics - Liouville's Equation, Gibbs Distribution, Ensembles

    • 2.1 Statistical Ensemble

    • 2.2 Liouville's Theorem

    • 2.3 Gibbs Distribution

    • 2.4 Canonical Ensemble
  • 4

    Lecture 3: Thermodynamic Approach to Phase Transitions - Ideal Gas, Van Der Waals Fluid, Reentrant PT

    • 3.1 Statistical Physics Machinery

    • 3.2 Example of Ideal Gas

    • 3.3 Van Der Waals Equation

    • 3.4 Liquid Gas Phase Transition

    • 3.5 Reentrant Phase Transitions

    • 3.6 Gravitational Meissner Effect

    • Tutorial 3

    • Solutions 3
  • 5

    Lecture 4: Ising Model, Order Parameter, Mean Field Theory, Critical Exponent Beta

    • 4.1 Microscopics of Phase Transitions

    • 4.2 Ising Model

    • 4.3 Mean Field Theory

    • 4.4 Critical Temperature

    • 4.5 Critical Exponent Beta

    • Tutorial 4

    • Solutions 4

    • Exercises 4
  • 6

    Lecture 5: Critical Exponents, Landau's Theory, Hubbard-Stratonovich Transformation

    • 5.1 MFT for Ising Model

    • 5.2 Other Critical Exponents

    • 5.3 Landau Theory

    • 5.4 Hubbard-Stratonovich Transformation

    • Tutorial 5

    • Solutions 5

    • Exercises 5
  • 7

    Lecture 6: Spin-Spin Correlation Function, Correlation Length, Landau-Ginsburg Functional

    • 6.1 Ising Phase Transition

    • 6.2 Correlation Function

    • 6.3 From Ising to Field Theory

    • 6.4 Lattice Fourier Transform

    • 6.5 Landau-Ginsburg Functional

    • Tutorial 6

    • Solutions 6
  • 8

    Lecture 7: Wilsonian Renormalization 1 - Basic Idea, Integration Over Fast Modes, Flowing Couplings

    • 7.1 Dimensional Analysis

    • 7.2 Idea of Wilsonian Renormalization

    • 7.3 Integration Over Fast Modes

    • 7.4 Flowing Couplings
  • 9

    Lecture 8: Wilsonian Renormalization 2 - Explicit Calculation, Cumulant Expansion, RG Equations

    • 8.1 Cumulant Expansion

    • 8.2 Feynman Diagrams

    • 8.3 RG Equations 1

    • 8.4 RG Equations 2
  • 10

    Lecture 9: Wilsonian Renormalization 3 - Triumph, Wilson-Fisher Fixed Point, Critical Exponents

    • 9.1 RG Flow Analysis

    • 9.2 Gaussian Fixed Point

    • 9.3 Wilson-Fisher Fixed Point

    • 9.4 Critical Exponents 1

    • 9.5 Critical Exponents 2

    • Tutorial 9.1

    • Solutions 9.1

    • Tutorial 9.2

    • Solutions 9.2
  • 11

    Lecture 10: Vector Model, Goldstone Molds, CMW Theorem and Lower Critical Dimension

    • 10.1 Summary of Ising

    • 10.2 Vector Model

    • 10.3 Goldstone Modes

    • 10.4 CMW Theorem

    • Exercises 10
  • 12

    Lecture 11: Near d=2, Vortices, Kosterlitz-Thoules Phase Transition

    • 11.1 Nonlinear Sigma Model

    • 11.2 Two Fields in Two Dimensions

    • 11.3 Vortices

    • 11.4 Kosterlitz-Thoules Phase Transition
  • 13

    Lecture 12: Monte Carlo Methods, Sampling, Markov Chain, Single-Spin-Flip Metropolis Algorithm

    • 12.1 Setting Up the Problem

    • 12.2 Monte Carlo Methods

    • 12.3 Importance Sampling and Markov Chain

    • 12.4 Single-Spin-Flip Algorithm
  • 14

    Lecture 13: Equilibrium & Measurement, Monte Carlo for the 2D Ising Model, Finite-Size Scaling

    • 13.1 Equilibrium and Measurement

    • 13.2 2D Ising Simulation

    • 13.3 Calculating Critical Properties

    • 13.4 X-Y Model

    • Tutorial 13

    • Tutorial Python Files 13

    • Solutions 13
  • 15

    Lecture 14: Bonus Lecture - Black Hole Thermodynamics

    • 14.1 Motivation

    • 14.2 Black Hole Mechanics and Hawking Radiation

    • 14.3 Hawking Temperature

    • 14.4 Partition Function and Black Hole Entropy

    • 14.5 Hawking-Page Phase Transition

    • Tutorial 14

    • Solutions 14