A projection method for statics and dynamics of lattice spin systems

TL;DR

This paper introduces a Monte Carlo projection method for analyzing static and dynamic properties of lattice spin systems, demonstrated on the 3D 3-state Potts model and its metastable decay.

Contribution

The paper presents a novel projection-based Monte Carlo sampling technique for studying lattice spin systems' dynamics and statics, focusing on slow variables.

Findings

Effective analysis of equilibrium properties of the 3D 3-state Potts model.

Insight into metastable decay processes in the kinetic Potts model.

Method demonstrates accurate projection onto order-parameter subspace.

Abstract

A method based on Monte Carlo sampling of the probability flows projected onto the subspace of one or more slow variables is proposed for investigation of dynamic and static properties of lattice spin systems. We illustrate the method by applying it, with projection onto the order-parameter subspace, to the three-dimensional 3-state Potts model in equilibrium and to metastable decay in a three-dimensional 3-state kinetic Potts model.