The self-organized multi-lattice Monte Carlo simulation

The self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of devised simulation method is the artificial dynamics consisting of the single-spin-flip algorithm of Metropolis supplemented by the random walk in the temperature space. The walk is biased to the critical region through the feedback equation utilizing the memory-based filtering recursion instantly estimating the energy cumulants. The simulations establish that the peak of the temperature probability density function is located nearly the pseudocritical temperature pertaining to canonical equilibrium. In order to eliminate the finite-size effects, the self-organized approach is extended to multi-lattice systems, where feedback is constructed from the pairs of the instantaneous running fourth-order cumulants of the magnetization. The replica-based simulations indicate that several properly chosen steady statistical distributions of the self-organized Monte Carlo systems resemble characteristics of the standard self-organized critical systems.