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Dr Anson cheung

Teaching 2011

Part III Phase Transitions and Collective Phenomena

As a theoretical option, this course will prove challenging to students without a mathematical background. Although the course will develop methods of statistical field theory from scratch, students will benefit from having attended either the Quantum Condensed Matter Field Theory or Quantum Field Theory course in Part III.

Introduction to Critical Phenomena:

Phase transitions, order parameters, response functions, critical exponents and universality.

Ginzburg-Landau Theory:

Mean-field theory; spontaneous symmetry breaking; Goldstone modes, and the lower critical dimension; fluctuations and the upper critical dimension; correlation functions; Ginzburg criterion.

Scaling Theory and the Renormalisation Group:

Self-similarity and the scaling hypothesis; Kadanoff's Heuristic Renormalisation Group (RG); Gaussian model; Fixed points and critical exponent identities; Wilson's momentum space RG, relevant, irrelevant and marginal parameters; Epsilon- expansions.

Topological Phase Transitions:

XY-model; algebraic order; topological defects; Kosterlitz-Thouless transition and superfluidity in thin films.

Lecture Notes:

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5

Problem Set 1
Problem Set 2

Extra Problems for Examination practice

Complete Notes including problem sets

Summary Notes from lectures

Supplementary reading:

Statistical Physics of Fields, Kardar M (CUP 2007)
Principles of Condensed Matter Physics, Chaikin P M & Lubensky T C (CUP 1995)
Scaling and Renormalisation in Statistical Physics, Cardy J (CUP 1996)