ICFP Stat Physics 2016
From Werner KRAUTH
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[[ICFP Stat Physics 2016 infos| Look here for practical information]] | [[ICFP Stat Physics 2016 infos| Look here for practical information]] | ||
- | ==Week 5: Two-dimensional Ising model: From Ising to Onsager== | + | ==Week 5 (5 October 2016): Two-dimensional Ising model: From Ising to Onsager== |
* [http://www.lps.ens.fr/~krauth/images/8/8d/TD05_ICFP_2016.pdf Tutorial 05: Peierls argument for spontaneous symmetry breaking in two and higher dimensions.] | * [http://www.lps.ens.fr/~krauth/images/8/8d/TD05_ICFP_2016.pdf Tutorial 05: Peierls argument for spontaneous symmetry breaking in two and higher dimensions.] | ||
* [http://www.lps.ens.fr/~krauth/images/b/b9/HW05_ICFP_2016.pdf Homework 05: Thouless (!) argument; transfer matrix for the two-dimensional Ising model on a stripe.] | * [http://www.lps.ens.fr/~krauth/images/b/b9/HW05_ICFP_2016.pdf Homework 05: Thouless (!) argument; transfer matrix for the two-dimensional Ising model on a stripe.] |
Revision as of 16:37, 9 October 2016
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
Week 5 (5 October 2016): Two-dimensional Ising model: From Ising to Onsager
- Tutorial 05: Peierls argument for spontaneous symmetry breaking in two and higher dimensions.
- Homework 05: Thouless (!) argument; transfer matrix for the two-dimensional Ising model on a stripe.
- PDF of Mathematica notebook file useful for Lecture 05 and Homework 05.
NB: I was contacted about periodic boundary conditions. Please look into the Homework file first, then note that the transfer matrix does not know whether periodic boundary conditions are assumed in x. It does know whether there are periodic boundary conditions in y.
References for Week 5:
- R. Peierls, Proceedings of the Cambridge Philosophical Society, 32, 477 (1936) (famous loop-counting argument establishing spontaneous symmetry breaking in the two-dimensional Ising model below a finite temperature)
- C. Bonati, Eur. J. Phys. 35, 035002 (2014) (generalization of the Peierls argument to higher dimensions)
- M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific) section 6.1 (Transfer matrix for the two-dimensional Ising model, Onsager's solution)
- T D Schultz, D C Mattis, E Lieb, "Two-dimensional Ising model as a soluble problem of many fermions" Reviews of Modern Physics (1964) (Authoritative account of Onsager's solution).
Week 4 (28 September 2016): Physics in one dimension - Hard spheres and the Ising model
- Tutorial 04: One-dimensional short-range interacting systems with phase transitions (!).
- Homework 04: Transfer matrices for hard spheres, variations on a theme. NB: Figures updated for clarity on 30 Sep 2016
References for Week 4:
- W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) p. 269ff (hard-sphere partition function using the double substitution).
- M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific) p. 145f (some background material on the virial expansion), p. 77 ff (Ising chain, although our treatment was considerably different).
- R. H. Swendsen, "Statistical mechanics of colloids and {Boltzmann's} definition of the entropy" American Journal of Physics 74, 187 (2006) (a good discussion of the Gibbs phenomenon)
- D. J. Thouless, "Long-range order in one-dimensional Ising systems" Physical Review 187, 732 (1969) (Ingenious discussion of the 1/r^2 Ising model)
- J. M. Kosterlitz, "Kosterlitz-Thouless physics: a review of key issues" Rep. Prog. Phys. 79 026001 (2016) (first two pages only, discussion and historical context for the Thouless paper. This is elementary to follow.).
- C. Kittel, American Journal of Physics 37, 917 (1969) (First exercise of Tutorial 4)
- J. A. Cuesta and A. Sanchez, J. Stat. Phys. 115, 869 (2004) (Third exercise of Tutorial 4, generalized Kittel model)
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:
- Kerson Huang, "Statistical Mechanics 2nd edition" (1987) (Tutorial Problem 1).
- L. Pauling, J. Am. Chem. Soc. 12 (2680-2684), 1935.(Tutorial Problem 2 on residual entropy of ice).
- Bramwell, Gingras, Science 294, 1495 ( 2001) (Spin ice in pyrochlore).
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)