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Elements of Phase Transitions and Critical Phenomena$
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Hidetoshi Nishimori and Gerardo Ortiz

Print publication date: 2010

Print ISBN-13: 9780199577224

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199577224.001.0001

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Numerical methods

Numerical methods

(p.258) 11 Numerical methods
Elements of Phase Transitions and Critical Phenomena

Hidetoshi Nishimori

Gerardo Ortiz

Oxford University Press

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

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