# ICFP Stat Physics 2017

### From Werner KRAUTH

This is the homepage for the ICFP course: Statistical Physics: Concepts and Applications that is running from 4 September 2017 through 18 December 2017. Lectures start at 8:30, on Monday mornings, and tutorials at 10:45.

Lectures: Werner KRAUTH

Tutorials (TD): Olga PETROVA, Jacopo DE NARDIS

Look here for practical information

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## Week 1 (4 September 2017): Probability theory

- Tutorial 01: Characteristic functions / Stable distributions (with solutions)
- Homework 01: Chebychev inequality / Rényi formula / Lévy distribution

References for Week 1:

- L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005) part 1
- W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) Section 1.3.4 only - Error intervals from Chebychev inequality.

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## Week 2 (11 September 2017): Statistical inference

- Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer
- Homework 02: From Maximum Likelihood to Bayes statistics Useful program:

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) Section 1.3.4 only

Further References for Week 2:

- 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.

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## Week 3 (18 September 2017): Statistical mechanics and Thermodynamics

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## Week 4 (25 September 2017): Phases and phase transitions: Van der Waals theory

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## Week 5 (02 October 2017): Hard spheres and the Ising model in one dimension (Transfer matrix 1/2)

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## Week 6 (09 October 2017): Two-dimensional Ising model: From Ising to Onsager (Transfer matrix 2/2)

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## Week 7 (16 October 2017): Two-dimensional Ising model: From Kramers & Wannier to Kac & Ward (Low- and high-temperature expansions)

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## Week 8 (23 October 2017): The three pillars of mean-field theory (Transitions and order parameters 1/2)

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## Week 9 (06 November 2017): Landau theory (Transitions and order parameters 2/2)

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## Week 10 (13 November 2017): Kosterlitz-Thouless physics in two dimensions: The XY model (Transitions without order parameters 1/2)

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## Week 11 (20 November 2017): Kosterlitz-Thouless physics in two dimensions: KTHNY Melting theory (Transitions without order parameters 2/2)

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## Week 12 (27 November 2017): The renormalization group - an introduction

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## Week 13 (04 December 2017): Quantum statistics 1/2: Ideal Bosons

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## Week 14 (11 December 2017): Quantum statistics 2/2: 4He and the 3D Heisenberg model, Non-classical rotational inertia

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## Week 15 (18 December 2017): The Fluctuation-Dissipation theorem (an introduction)

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## References

Lecture notes are not yet available. A few essential references are given each week. ICFP students can access these references from within the Department (you may for example connect to Web of Science, and download them from there). You may also ask the library staff at 29 rue d'Ulm.

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## 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)