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Markov Chain Analysis of Single Spin Flip Ising Simulations

Author

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  • Michael Hennecke

    (Computing Center, University of Karlsruhe, D-76128 Karlsruhe, Germany;
    Institute for Theoretical Physics, Cologne University, D-50923 Köln, Germany)

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.

Suggested Citation

  • Michael Hennecke, 1997. "Markov Chain Analysis of Single Spin Flip Ising Simulations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 207-227.
    • Handle: RePEc:wsi:ijmpcx:v:08:y:1997:i:02:n:s0129183197000199
    DOI: 10.1142/S0129183197000199
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    Cited by:

    1. Hennecke, Michael, 1997. "Survivors in the two-dimensional Potts model: zero-temperature dynamics for Q = ∞," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 519-528.

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