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Work in progress (modified: October 2023)

Lectures on Statistical Physics

• Introduction
• Gibbs ensembles
• Equilibrium and irreversibility
• Non interacting systems, bose and fermi gases
• Paramagnetism and diamagnetism
• Interacting gases: virial expansion
• Lattice models
• Phase transitions
• Twodimensional ising model
• Problems, exercises and applications
  • probability theory
  • boltzmann distribution
  • quantum gases, bose and fermi non-interacting systems
  • interacting systems
  • selected problems
• Homework assignments
• Solution to exam exercises

Bibliography

• Landau, D. and Lifshitz, E., Statistical Physics (Pergamon Oxford, 1980).
• Kardar, M., Statistical Physics, vol. 1 Particles, vol. 2 Fields (Cambridge, 2007).
• Sethna, J. P., Statistical Mechanics, Entropy, Order Parameter and Complexity (Oxford, 2021).
• Schwabl, F., Statistical Mechanics (Springer, 2006).

Syllabus (2023-2024)

This course is intended to students who followed a first statistical physics course at the level of the classical book by Kittel, “Thermal physics” (1980).

In addition to plenary lectures, the course proposes complementary exercises (marked EX), and a series of “applications”, intended to give you an idea of the diversity of domains for which statistical mechanics methods are useful (even outside the traditional physical field), including problems whose solution needs numerical methods.

Homework assignments are given in the section “Problems, exercises and applications”.

Principles

• Introduction: from the microscopic states to thermodynamics
• Density matrix and quantum statistics, Gibbs ensembles
• Ideal gas, rotation and vibration of molecules, two level system
• Quantum gases, Bose condensation, photons and phonons, Debye
• Fermi distribution, degenerated electron gas
• Pauli paramagnetism, Landau diamagnetism

Interactions

• Diluted systems, virial expansion, real gases, trapped fermions
• Lattice systems, Ising model, transfer matrix, mean field, Monte-Carlo
• XY model and the Kosterlitz-Thouless transition
• Onsager exact solution of the twodimensional ising model

Phase transitions and fluctuations

• Phenomenology and scaling laws
• Order parameter and Landau free energy, symmetry breaking
• Linear response and correlations