Phase Transitions

Statistical Mechanics & Phase Transitions

[Spring 2014 - MS Physics - IST - Lisbon]

Syllabus

0.Introduction

Historical developments | What you will be able to do by the end of the semester

1.Thermodynamics and Statistical Mechanics

Some models | Principle of entropy maximization | The role of the thermodynamic limit | Spontaneous symmetry and ergodicity breaking

2. Landau Theory of phase transitions

Landau theory | Ginzburg-Landau theory | Fluctuations - Break down of Landau Theory | Examples of mean field theories

3. Scaling

Anomalous dimensions | The scaling hypothesis | Finite size scaling

4. Ordered Phases

Breaking of continuous symmetries | Goldstone Theorem | Examples of Goldstone modes | The Higgs mechanism

5. Renormalization group

Kadanoff's construction | Main ideas of the RG | Momentum shell RG | epsilon-expansion

6. 2D Ising Model

High and low temperature expansions | Quantum to classical mapping | Quantum phase transitions - Transverse Field Ising Model

7. The Kosterlitz-Thouless transition

Topological defects | Spin-waves | Vortices

Biblio

N. Goldenfeld,

Lectures on Phase Transitions and the Renormalization Group | Frontiers in Physics, Perseus Books

G. Mazenko

Fluctuations Order & Defects | Wiley-VCH

K. Huang

Statistical Mechanics | John Wiley & Sons, New York.

P. Chaikin e T.C. Lubenski

Principles of Condensed Matter Physics | Cambridge University Press