Monte Carlo algorithms based on the number of potential moves

TL;DR

This paper introduces Monte Carlo algorithms that utilize the average number of potential moves increasing energy, enabling efficient sampling of microcanonical and canonical distributions with fast relaxation times.

Contribution

The paper proposes a novel Monte Carlo dynamics based on microcanonical averages of potential moves, improving sampling efficiency and relaxation times near critical points.

Findings

Fast relaxation time proportional to specific heat at critical temperature

Efficient sampling of microcanonical and canonical distributions

Useful for reweighting methods in thermodynamics

Abstract

We discuss Monte Carlo dynamics based on <N(sigma, Delta E)>_E, the (microcanonical) average number of potential moves which increase the energy by Delta E 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(sigma', E-E')>_E' / <N(sigma, 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.