Monte Carlo algorithms based on the number of potential moves

Abstract

We discuss Monte Carlo dynamics based on 〈N(σ, ΔE)〉E, the (microcanonical) average number of potential moves which increase the energy by ΔE in a single spin flip. The microcanonical average can be sampled using Monte Carlo dynamics of a single spin flip with a transition rate min(1, 〈N(σ′, E - E′)〉E′/〈N(σ, E′ - E)〉E) from energy E to E′. A cumulative average (over Monte Carlo steps) can be used as a first approximation to the exact microcanonical average in the flip rate. The associated histogram is a constant independent of the energy. The canonical distribution of energy can be obtained from the transition matrix Monte Carlo dynamics. This second dynamics has fast relaxation time - at the critical temperature the relaxation time is proportional to specific heat. The dynamics are useful in connection with reweighting methods for computing thermodynamic quantities.