Four lectures on computational statistical physics

TL;DR

This paper summarizes key concepts and methods in computational statistical physics, including sampling techniques, classical and quantum Monte Carlo methods, and applications to models like the Ising model, emphasizing simplicity and accessibility.

Contribution

It provides an accessible overview of computational methods in statistical physics, including perfect sampling and simplified algorithms for quantum Monte Carlo, with practical code resources.

Findings

Introduction of perfect sampling concept

Simplified quantum Monte Carlo algorithms

Illustration of physics unity through Ising model

Abstract

In my lectures at the Les Houches Summer School 2008, I discussed central concepts of computational statistical physics, which I felt would be accessible to the very cross-cultural audience at the school. I started with a discussion of sampling, which lies at the heart of the Monte Carlo approach. I specially emphasized the concept of perfect sampling, which offers a synthesis of the traditional direct and Markov-chain sampling approaches. The second lecture concerned classical hard-sphere systems, which illuminate the foundations of statistical mechanics, but also illustrate the curious difficulties that beset even the most recent simulations. I then moved on, in the third lecture, to quantum Monte Carlo methods, that underly much of the modern work in bosonic systems. Quantum Monte Carlo is an intricate subject. Yet one can discuss it in simplified settings (the single-particle free propagator, ideal bosons) and write direct-sampling algorithms for the two cases in two or three dozen lines of code only. These idealized algorithms illustrate many of the crucial ideas in the field. The fourth lecture attempted to illustrate aspects of the unity of physics as realized in the Ising model simulations of recent years. More details on what I discussed in Les Houches, and wrote up (and somewhat rearranged) here, can be found in my book, "Statistical Mechanics: Algorithms and Computations", as well as in recent papers. Computer programs are available for download and perusal at the book's web site www.smac.lps.ens.fr.