Random physics

Alberto Verga, research notebook

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Work in progress

Lectures on Statistical Physics


  • Landau, D. and Lifshitz, E., Statistical Physics (Pergamon Oxford, 1980). The best classical text on statistical physics.
  • Kardar, M., Statistical Physics, vol. 1 Particles, vol. 2 Fields (Cambridge, 2007). Clear presentation, interesting applications.
  • Sethna, J. P., Statistical Mechanics, Entropy, Order Parameter and Complexity (Oxford, 2006). Very intersting and up to date text with a wealth of applications; intermediate level.
  • Schwabl, F., Statistical Mechanics (Springer, 2006). Excellent presentation of the basis of statistical physics at a conceptual level. This book, primary addressed to undergraduate students, deal with more advanced subjects through well chosen applications. Highly recommended.

Syllabus (2018-2019)

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

In addition to pleanry lectures, the course proposes complementary exercises (marked EX), and a series of “applications”, sensed give you a grasp 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.

A list of homeworks is given in “Problems, exercises and applications”. Selected solution and complements can be found in


  • Statistical ensemble: from the microscopic states to thermodynamics
  • Density matrix and the microcanonical distribution of an isolated system
  • Gibbs ensembles
  • Gibbs distribution (classical and quantum); the partition function and the free energy
  • Thermodynamic quantities

Noninteracting systems

  • Energy equipartition
  • Ideal gas
  • Rotation and vibration of molecules
  • Bose distribution, photons and phonons, Debye, Bose condensation
  • Fermi distribution, degenerated electron gas
  • Pauli paramagnetism and mean field ferromagnetism
  • Landau diamagnetism


  • Ising model, low and high energy expansions in 2D
  • Cumulant expansion and virial coefficients
  • Van der Waals equation and liquid-gas transition
  • Bose and Fermi liquids

Phase transitions and fluctuations

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


  • From the binomial distribution to the large number and central limit theorems
  • Chaos, ergodicity and mixing
  • Mixing entropy and the Gibbs paradox
  • Maxwell demon and information theory
  • Two level systems
  • Quantum oscillator
  • Monte Carlo for the ising model
  • 2x2 random matrices, Wiener surmise
  • Lenard-Jones potential and molecular dynamics
  • White dwarf stars
  • Black hole entropy
  • Yang-Lee theory of phase transitions
  • Quantum spin in a transverse field