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Teaching 2024
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 Theories of Quantum Matter or
Quantum Field Theory courses 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.
Quantum Phase Transitions:
Classical/Quantum Mapping; the
Dynamical Exponent; Quantum Rotors; Haldane Gap; Asymptotic Freedom;
Quantum Criticality
Lecture Notes (to populate over the term):
Preface
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Problem Set 1
Problem Set 2
Problem Set 3
Lecture 1 slides
Lecture 2a handwritten
Lecture 2b handwritten
Lecture 3 handwritten
Lecture 4 handwritten
Lecture 4a handwritten
Lecture 5 handwritten
Lecture 6 handwritten
Lecture 7 handwritten
Lecture 8 handwritten
Lecture 9 handwritten
Lecture 10 handwritten
Lecture 11 handwritten
Lecture 12 handwritten
Bonus lecture handwritten
Complete Notes
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)
Quantum Field Theory and Condensed Matter: An Introduction, Shankar R (CUP 2017)
Phase Transitions and Renormalization Group, Zinn-Justin J (OUP 2013)
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