ICFP Stat Physics 2016

From Werner KRAUTH

This is the homepage for the ICFP course: Statistical Physics: Concepts and Applications.

Lectures: Werner KRAUTH

Practicals & Homeworks: Maurizio FAGOTTI, Olga PETROVA

• Week 1 (7 September 2016): Probability theory
  • Homework 01: Chebychev inequality / Rényi formula / Lévy distribution Useful programs:
    • Renyi.py: Probability distribution of a sum of uniform random numbers
    • Levy.py: Probability distribution of a sum of random variables that may (or may not) have an infinite variance
  • Tutorial 01: Characteristic functions / Stable distributions

Syllabus

• Week 1: Probability theory
  • Probabilities, probability distributions, sampling
  • Random variables
  • Expectations
  • Inequalities (Markov, Chebychev, Hoeffding)
  • Convergence of random variables (Laws of large numbers, CLT)
  • Lévy distributions
• Week 2: Statistics (statistical inference, estimation, learning)
  • Point estimation, confidence intervals
  • Bootstrap
  • Method of moments
  • Maximum likelihood, Fisher information
  • Parametric Bootstrap
  • Bayes statistics
• Week 3: Statistical mechanics and Thermodynamics
  • Rapid overview on the connection between statistical mechanics and thermodynamics
  • lightning review of ensembles and
  • lightning review of the main physical quantities (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).
• Week 4: Physics in one dimension
  • One-dimensional hard spheres, virial expansion, partition function
  • One-dimensional Ising model
  • Transfer matrix
  • Kittel model
  • ~Chui-Weeks model: Infinite-dimensional transfer matrix
  • One-dimensional Ising model with 1/r^2 interactions
• Week 5: Two-dimensional Ising model: From Ising to Onsager
  • Peierls argument, ~Kramers-Wannier relation
  • Two-dimensional transfer matrix (following Schultz et al)
  • ~Jordan-Wigner transformation
  • Free energy calculation
  • Spontaneous magnetization, zero-field susceptibility
  • Kaufman, ~Ferdinand-Fisher, Beale
• Week 6: Two-dimensional Ising model: From Kac and Ward to Saul and Kardar
  • Van der Waerden, low-temperature and high-temperature expansions
  • Duality
• Week 7: Physics in two dimensions (~Kosterlitz-Thouless physics): XY (planar rotor) model
  • Peierls argument
  • ~Mermin-Wagner theorem
  • Non-universality
• Week 8: Physics in two dimensions (~Kosterlitz-Thouless physics): Particle systems, superfluids
• Week 09: Physics in infinite dimensions: Mean-field theory, Scaling
• Week 10: Physics in infinite dimensions: Landau theory
• Week 11: Renormalization group
• Week 12: The Solid state: Order parameters, correlation functions
• Week 13: Quantum systems - bosons.
• Week 14: Quantum systems - spin systems
• Week 15: Equilibrium and transport, Fluctuation-dissipation theorem.

References

Lecture notes will be available before each course.

Books

• L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005)
• W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006)
• M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific)
• L. D. Landau, E. M. Lifshitz, "Statistical Physics" (Pergamon)