Advanced Statistical Physics (P817), Spring 2018

Advanced Statistical Physics (P817), Spring 2018

Instructor: Romain Vasseur, Assistant Professor
office: Hasbrouck 405A
email: rvasseur[at]umass[dot]edu
office hours: by appointment and email, or visit my office

Lectures: MW 2.30-3.45am, room: Has 107

Suggested reading materials:

  • Scaling and Renormalization in Statistical Physics, John Cardy,  Cambridge University Press
  • Statistical Physics of Fields, Kardar, Cambridge University Press
  • Lectures on Phase Transitions and the Renormalization Group, Nigel Goldenfeld,  Frontiers in Physics Series (Vol. 85), Westview Press
  • Principles of Condensed Matter Physics, P.M. Chaikin & T.C. Lubensky, Cambridge University Press
  • Phase transitions and Renormalization Group, Jean Zinn-Justin, Oxford Graduate Texts

Website: https://blogs.umass.edu/rvasseur/teaching/. Course materials will also be made available on Moodle.

Grading:
The course grade will be based 40% on the homework, 30% on a take-home exam, and 30% on a final term paper.

Topics:

  • Introduction: Critical phenomena and simple models. Mean-field theory.
  • Ginzburg-Landau theory: fluctuations, Ginzburg criterion, upper/lower critical dimensions, Goldstone modes.
  • The Renormalization Group
  • The perturbative RG:
    • Operator product expansions
    • epsilon expansion
    • O(N) model and Large N limit
  • XY model: Topological defects, Coulomb gas and Berezinskii-Kosterlitz–Thouless transition
  • Advanced topics (time permitting):
    • Nonlinear sigma model
    • Random Systems
    • (Brief) Introduction to conformal field theory

Lecture Notes:

  1. Critical Phenomena
  2. Ginzburg-Landau theory & Fluctuations
  3. The Renormalization Group
  4. Perturbative RG
  5. KT transition
  6. Nonlinear sigma model
  7. Disordered systems
  8. CFT

Problem Sets:

  1. HW1: Simple models and Mean Field theory
  2. HW2: Ginzburg-Landau theory
  3. HW3: Scaling and RG
  4. HW4: Perturbative RG
  5. HW5: XY model

Solutions available on Moodle, or upon request by email.

Final Exam: Exam

Suggestions for final project:

  • Disordered systems: replica trick, Harris criterion, Imry-Ma argument
  • RG in high-energy physics vs statistical mechanics
  • Quantum criticality: quantum to classical mapping, example: transverse field Ising chain
  • Exact solution of the 2D Ising model using Majorana fermions (possibility to collaborate with “quantum criticality”)
  • Percolation: mapping onto Potts model, critical behavior
  • Polymers: limit n–> 0 of the O(n) model, critical behavior
  • Surface critical behavior (Cardy)
  • Topological terms in non-linear sigma models
  • Spin glasses
  • Momentum-shell RG (compare to OPE approach developed in class)
  • Critical dynamics: reaction diffusion models (Cardy)
  • Monte Carlo simulations and finite-size scaling: write a MC code for the 2D Ising model and extract critical exponents
  • Dynamic of growing surfaces, KPZ equation (Kardar)
  • Integrable statistical mechanics models
  • Conformal Field Theory (Finite size scaling)
  • CFT (global conformal invariance, correlation functions + overview in 2d)
  • Neural networks: Hopfield model
  • Scaling in non-equilibrium systems (Goldenfeld)
  • Lee-Yang theorem
  • Caldeira-Leggett model (qubit in dissipative environment)

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