Dynamic Canonical and Microcanonical Transition Matrix Analyses of Critical Behavior

TL;DR

This paper introduces a family of transition matrix techniques that adaptively control temperature or energy variations, improving accuracy over standard methods in analyzing critical behavior in statistical systems.

Contribution

The authors develop a novel family of transition matrix methods that automatically adjust parameters, surpassing traditional multi-chain approaches in accuracy for single Markov chain analyses.

Findings

Enhanced accuracy in critical behavior analysis.

Effective automatic control of temperature and energy variations.

Superior performance compared to standard transition matrix methods.

Abstract

By monitoring the sampling of states with different magnetizations in transition matrix procedures a family of accurate and easily implemented techniques are constructed that automatically control the variation of the temperature or energy as the calculation proceeds. The accuracy of the method for a single Markov chain exceeds that of standard transition matrix procedures that accumulate elements from multiple chains.