Chapter

Numerical methods

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print December 2010 | ISBN: 9780199577224
Published online January 2011 | e-ISBN: 9780191722943 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577224.003.0011

Series: Oxford Graduate Texts

Numerical methods

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This chapter introduces a few typical numerical methods used in modern studies of phase transitions and critical phenomena in spin systems. The first section describes the stochastic dynamics of a generic system with discrete degrees of freedom following the master equation. This section serves as a theoretical basis for the Monte Carlo method that includes the heat bath and Metropolis algorithms of configuration updates. Another useful numerical technique is the transfer matrix method, described in the last section, and which is applied for numerically exact evaluation of the free energy and related physical quantities.

Keywords: stochastic dynamics; master equation; Monte Carlo method; heat bath algorithm; Metropolis algorithm; transfer matrix

Chapter.  4159 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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