A Cluster Controller for Transition Matrix Calculations

TL;DR

This paper introduces a method to efficiently generate temperature schedules for transition matrix calculations in Ising models by monitoring Wolff cluster sizes, and proposes a technique combining cluster and single-spin flip steps to construct a unified transition matrix.

Contribution

It presents a novel approach to optimize temperature schedules using Wolff cluster sizes and combines cluster and single-spin flip methods for transition matrix construction.

Findings

Optimized temperature schedules relate to fractal structures of clusters.

The combined method improves transition matrix calculations.

Potential for faster simulations in statistical physics.

Abstract

We demonstrate that a temperature schedule for single-spin flip transition matrix calculations can be simply and rapidly generated by monitoring the average size of the Wolff clusters at a set of discrete temperatures. Optimizing this schedule yields a potentially interesting quantity related to the fractal structure of Ising clusters. We also introduce a technique in which the transition matrix is constructed at a sequence of discrete temperatures at which Wolff cluster reversals are alternated with certain series of single-spin flip steps. The single spin-flip transitions are then employed to construct a single transition matrix.