Course curriculum

  • 1

    Course information

    • Course outline

    • Recording of course introduction (morning)

    • Recording of course introduction (afternoon)
  • 2

    Theme songs

    • chaossong

    • groundstatez

    • thermalization

    • untitled #1

    • untitled #2
  • 3

    Tutorials & homework

    • Homework 1

    • Homework 2

    • Homework 3

    • Tutorial 2

    • Tutorial 2 solutions

    • Tutorial 3

    • Tutorial 3 Solutions

    • Tutorial 4

    • Tutorial 4 solutions

    • Tutorial 5

    • Tutorial 5 Solutions

    • Tutorial 6

    • Tutorial 6 solutions

    • Tutorial 7

    • Tutorial 7 solutions

    • Tutorial 8

    • Tutorial 8 solutions
  • 4

    Written component

    • Written Component

    • Simulation Component

    • Article by Fisher
  • 5

    Week 1: Review of statistical mechanics

    • 1 - Phase space formalism

    • 2a - Microstates and macrostates

    • 2b - Microstates and macrostates

    • 3a - Liouville’s theorem

    • 3b - Liouville's theorem

    • 4a - Time and ensemble average

    • 4b - Time and ensemble average

    • 5 - Ensembles

    • 6a - Statistics of simple gases

    • 6b - Maxwell-Boltzmann statistics
  • 6

    Week 2: Phase Transitions, Ising Model, Mean Field Theory

    • 1a - Thermodynamic Approach to Phase Transitions

    • 1b - Van der Waals Model

    • 1c - Geogebra applet

    • 2a - Microscopic Theory of Phase Transitions

    • 2b - Critical exponents

    • 2c - Geogebra applet

    • 3 - Ising Model

    • 4a - Mean Field Theory

    • 4b - Mean Field Theory

    • 4c - Geogebra applet
  • 7

    Week 3: Landau theory, scaling hypothesis, introduction to the RG

    • 1a - Landau theory

    • 1b - Landau theory

    • 2a - Scaling hypothesis

    • 2b - Scaling hypothesis

    • 3 - Intro to RG

    • 4 - Block-spin renormalisation

    • 5 - From Ising model to field theory

    • 6a - Momentum space

    • 6b - Lattice Fourier transform

    • 6c - Momentum space partition function
  • 8

    Week 4: Momentum-space renormalisation

    • 1 - The Gaussian model

    • 2a - Momentum-space renormalisation

    • 2b - Momentum space RG (step 1)

    • 2c - Momentum space RG (step 2)

    • 3 - Fixed points and critical exponents

    • 4a - ϕ⁴ model

    • 4b - Cumulant expansion

    • 4c - Calculations for the rescaling step

    • 4d - Wilson–Fisher fixed point

    • 5a - Vector Model

    • 5b - Kosterlitz-Thouless (KT) Transition

    • Additional resources

    • Resource - David Kubiznak's notes on Vector Model and KT
  • 9

    Week 5: Quantum Phase Transitions

    • 1 - Introduction to Quantum Phase Transitions

    • 2a - Quantum Phase Transition Examples

    • 2b - Quantum Ising Model: Mean Field Theory

    • 2c - Fermionic Operators

    • 3a - Quantum Monte Carlo

    • 3b - Simulating Classical and Quantum Systems

    • 4 - (Optional) Fermionic QMC Algorithms