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
Look here for practical information
Contents |
Week 3 (21 September 2016): Statistical mechanics and Thermodynamics
- Tutorial 03: Two-level systems and the entropy of ice. Maxwell's distribution.
- NB: Homework break for this week, graded homeworks will start in week 4.
References for Week 3: TBA
Week 2 (14 September 2016): Statistical inference
- Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer
- Homework 02: From Maximum Likelihood to Bayes statistics Useful program:
- NB: Homework 02 will be corrected, but does not count for the final grade ("dry run"). Due on 21 September 2016, return of corrected copies: 28 September 2016.
- Bayes_tank.py: Bayesian approach to solving the German Tank problem
References for Week 2:
- L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005) part 2
- W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) p. 58 only ;)
- B. Efron, "Maximum likelihood and decision theory" Ann. Statist. 10, 340, 1982.
- B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, 1-26, 1979.
- P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American 248, no. 5, pp. 116-130, 1983.
Week 1 (7 September 2016): Probability theory
- Tutorial 01: Characteristic functions / Stable distributions
- Homework 01: Chebychev inequality / Rényi formula / Lévy distribution
- NB: Homework 01 will be corrected, but does not count for the final grade ("dry run"). Due on 14 September 2016, return of corrected copies: 21 September 2016.
- Useful program: Renyi.py: Probability distribution of a sum of uniform random numbers
- Useful program: Levy.py: Probability distribution of a sum of random variables that may (or may not) have an infinite variance
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
- Ensembles and physical observables (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)
