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Markov chain analysis using Fortran 90

By  and Michael Hennecke and Michael Hennecke

Abstract

this article, the design of a Fortran 90 program to investigate the Markov properties of Monte Carlo simulation methods for the Ising model is presented. The formal specification of the transition matrices for these simulation methods can be elegantly expressed using Fortran 90 array features. Additionally, a sparse matrix type is defined to hold the building blocks of the transition matrices. By encapsulating this type and the necessary operations on it in a MODULE, the original program is transparently extended to address much larger problem sizes. 1 Physical background Monte Carlo simulation is a powerful tool that is widely used in statistical physics[1], and the Ising model[2] is one of the best-known model systems studied by such simulations. It can be informally described as follows: A square lattice is occupied by N = l 1 \Theta l 2 spins, and periodic boundary conditions are applied to minimize surface effects. Each spin can have only two possible values: +1 or UP, and \Gamma1 or DOWN. It interacts only with its four nearest neighbors, the energy of a "bond" between two spins is defined to be \GammaJ \Delta S i \Delta S

Year: 1996
OAI identifier: oai:CiteSeerX.psu:10.1.1.41.5593
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