Monte Carlo without Chains

TL;DR

This paper introduces a novel sampling method for spin systems that generates independent samples without Markov chains, using a nested sublattice approach and concurrent marginal computations, demonstrated on complex models like the 3D spin glass.

Contribution

The method provides a chain-free, efficient sampling technique for spin systems, with concurrent marginal calculations and error correction via weights, applicable to complex models.

Findings

Samples are independent and generated efficiently.

Method successfully applied to 3D Edwards-Anderson spin glass.

Cost per sample scales with the number of spins.

Abstract

A sampling method for spin systems is presented. The spin lattice is written as the union of a nested sequence of sublattices, all but the last with conditionally independent spins, which are sampled in succession using their marginals. The marginals are computed concurrently by a fast algorithm; errors in the evaluation of the marginals are offset by weights. There are no Markov chains and each sample is independent of the previous ones; the cost of a sample is proportional to the number of spins (but the number of samples needed for good statistics may grow with array size). The examples include the Edwards-Anderson spin glass in three dimensions.