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4 - Importance sampling Monte Carlo methods

Published online by Cambridge University Press:  24 November 2021

David Landau  and
Kurt Binder
David Landau
Affiliation:
University of Georgia
Kurt Binder
Affiliation:
Johannes Gutenberg Universität Mainz, Germany
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Summary

In this chapter we want to introduce simple importance sampling Monte Carlo techniques as applied in statistical physics and which can be used for the study of phase transitions at finite temperature. We shall discuss details, algorithms, and potential sources of difficulty using the Ising model as a paradigm. It should be understood, however, that virtually all of the discussion of the application to the Ising model is relevant to other models as well, and a few such examples will also be discussed. Other models as well as sophisticated approaches to the Ising model will be discussed in later chapters. The Ising model is one of the simplest lattice models which one can imagine, and its behavior has been studied for a century. The simple Ising model consists of spins which are confined to the sites of a lattice and which may have only the values +1 or −1.

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A Guide to Monte Carlo Simulations in Statistical Physics , pp. 80 - 160
Publisher: Cambridge University Press
Print publication year: 2021

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