Markov Chain Analysis of Single Spin Flip Ising Simulations

Michael Hennecke ()
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Michael Hennecke: Computing Center, University of Karlsruhe, D-76128 Karlsruhe, Germany;

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 02, 207-227

Abstract: The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often donotdefine ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities.

Keywords: Ising Model; Markov Chains; Ergodicity; Autocorrelation Times (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S0129183197000199

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