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The Self-Organized Multi-Lattice Monte Carlo Simulation

Author

Listed:
  • DENIS HORVÁTH

    (Department of Theoretical Physics and Astrophysics, University of P. J. Šafárik, Park Angelinum 9, 040 01 Košice, Slovak Republic)

  • MARTIN GMITRA

    (Department of Theoretical Physics and Astrophysics, University of P. J. Šafárik, Park Angelinum 9, 040 01 Košice, Slovak Republic)

Abstract

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called herenoncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

Suggested Citation

  • Denis Horváth & Martin Gmitra, 2004. "The Self-Organized Multi-Lattice Monte Carlo Simulation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(09), pages 1249-1268.
  • Handle: RePEc:wsi:ijmpcx:v:15:y:2004:i:09:n:s0129183104006674
    DOI: 10.1142/S0129183104006674
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    References listed on IDEAS

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    1. Perez, A.A, 2001. "Comment on “On the multinomial logic model” [Physica A 269 (1999) 9–15]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 606-606.
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