Using wavelets for fast Monte Carlo simulation of Ising systems with distribution matching

A new wavelet-based method is presented that improves the accuracy of a previously published wavelet-accelerated Monte Carlo analysis of the two-dimensional Ising model by one to two orders of magnitude in the critical and paramagnetic regions, and is up to ten times faster than the standard Metropolis algorithm. In the context of lattice simulations, successive levels of upscaling reduce the number of degrees of freedom, with corresponding gains in computational speed. Empirical results, for a variety of temperatures for a 32 × 32 lattice of binary spins, show that the resulting computational errors are reduced by running simulations at the thermodynamic temperature that minimizes the information-theoretic divergence between the Boltzmann equilibrium distributions of the original and coarse-grained systems. This optimal temperature relationship Monte Carlo method (OTRMC) may also benefit image processing applications, such as image restoration, that employ Monte Carlo simulations of Markov random fields.