THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

Denis Horváth () and Martin Gmitra ()
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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

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 09, 1249-1268

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.

Keywords: Monte Carlo simulation; self-organization; criticality; Ising model; damage spreading (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104006674

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