

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.
GinzburgLandau Theory:
Meanfield 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:
Selfsimilarity 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:
XYmodel; algebraic order; topological
defects; KosterlitzThouless transition and superfluidity in thin films.
Lecture Notes:
Preface
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)
