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THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

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

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MARTIN GMITRA

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

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https://doi.org/10.1142/S0129183104006674Cited by:3 (Source: Crossref)

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 here noncanonical 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.

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