Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation

A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity C are derived from derivatives of the partit...

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Bibliographic Details
Published inarXiv.org
Main Author Sasaki, Munetaka
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.08.2010
Subjects
Algorithms
Computer simulation
Computing time
Heat exchange
Internal energy
Monte Carlo simulation
Partitions
Partitions (mathematics)
Physics - Statistical Mechanics
Representations
Specific heat
Switching theory
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Summary:A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity C are derived from derivatives of the partition function. We also derive a formula for the exchange probability in the replica exchange Monte Carlo method. By combining the formulae with the Stochastic Cutoff method, we can greatly reduce the computational time to perform internal energy and heat capacity measurements and the replica exchange Monte Carlo method in long-range interacting systems. Numerical simulations in three dimensional magnetic dipolar systems show the validity and efficiency of the method.
ISSN:2331-8422
DOI:10.48550/arxiv.1001.1023