Metropolis algorithm and equienergy sampling for two mean field spin systems
Abstract
In this paper we study the Metropolis algorithm in connection with two mean--field spin systems, the so called mean--field Ising model and the Blume--Emery--Griffiths model. In both this examples the naive choice of proposal chain gives rise, for some parameters, to a slowly mixing Metropolis chain, that is a chain whose spectral gap decreases exponentially fast (in the dimension of the problem). Here we show how a slight variant in the proposal chain can avoid this problem, keeping the mean computational cost similar to the cost of the usual Metropolis. More precisely we prove that, with a suitable variant in the proposal, the Metropolis chain has a spectral gap which decreases polynomially in 1/N. Using some symmetry structure of the energy, the method rests on allowing appropriate jumps within the energy level of the starting state.
Keywords
Cite
@article{arxiv.0704.0906,
title = {Metropolis algorithm and equienergy sampling for two mean field spin systems},
author = {Bassetti Federico and Leisen Fabrizio},
journal= {arXiv preprint arXiv:0704.0906},
year = {2007}
}