ICFP Stat Physics 2016

From Werner KRAUTH

(Difference between revisions)
Jump to: navigation, search
Revision as of 09:33, 21 September 2016
Werner (Talk | contribs)

← Previous diff
Revision as of 15:56, 23 September 2016
Werner (Talk | contribs)

Next diff →
Line 51: Line 51:
* Week 3: Statistical mechanics and Thermodynamics * Week 3: Statistical mechanics and Thermodynamics
** Rapid overview on the connection between statistical mechanics and thermodynamics ** Rapid overview on the connection between statistical mechanics and thermodynamics
-** lightning review of ensembles and +** Ensembles and physical observables (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).
-** lightning review of the main physical quantities (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).+
* Week 4: Physics in one dimension * Week 4: Physics in one dimension
** One-dimensional hard spheres, virial expansion, partition function ** One-dimensional hard spheres, virial expansion, partition function
Line 58: Line 57:
** Transfer matrix ** Transfer matrix
** Kittel model ** Kittel model
-** ~Chui-Weeks model: Infinite-dimensional transfer matrix+** Chui-Weeks model: Infinite-dimensional transfer matrix
** One-dimensional Ising model with 1/r^2 interactions ** One-dimensional Ising model with 1/r^2 interactions
* Week 5: Two-dimensional Ising model: From Ising to Onsager * Week 5: Two-dimensional Ising model: From Ising to Onsager
-** Peierls argument, ~Kramers-Wannier relation+** Peierls argument, Kramers-Wannier relation
** Two-dimensional transfer matrix (following Schultz et al) ** Two-dimensional transfer matrix (following Schultz et al)
-** ~Jordan-Wigner transformation+** Jordan-Wigner transformation
** Free energy calculation ** Free energy calculation
** Spontaneous magnetization, zero-field susceptibility ** Spontaneous magnetization, zero-field susceptibility
-** Kaufman, ~Ferdinand-Fisher, Beale+** Kaufman, Ferdinand-Fisher, Beale
* Week 6: Two-dimensional Ising model: From Kac and Ward to Saul and Kardar * Week 6: Two-dimensional Ising model: From Kac and Ward to Saul and Kardar
** Van der Waerden, low-temperature and high-temperature expansions ** Van der Waerden, low-temperature and high-temperature expansions
** Duality ** Duality
-* Week 7: Physics in two dimensions (~Kosterlitz-Thouless physics): XY (planar rotor) model +* Week 7: Physics in two dimensions (Kosterlitz-Thouless physics): XY (planar rotor) model
** Peierls argument ** Peierls argument
-** ~Mermin-Wagner theorem+** Mermin-Wagner theorem
** Non-universality ** Non-universality
-* Week 8: Physics in two dimensions (~Kosterlitz-Thouless physics): Particle systems, superfluids+* Week 8: Physics in two dimensions (Kosterlitz-Thouless physics): Particle systems, superfluids
* Week 09: Physics in infinite dimensions: Mean-field theory, Scaling * Week 09: Physics in infinite dimensions: Mean-field theory, Scaling
* Week 10: Physics in infinite dimensions: Landau theory * Week 10: Physics in infinite dimensions: Landau theory

Revision as of 15:56, 23 September 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

Contents

Week 3 (21 September 2016): Statistical mechanics and Thermodynamics

References for Week 3: TBA

Week 2 (14 September 2016): Statistical inference

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


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)
Personal tools