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