Dynamic Canonical and Microcanonical Transition Matrix Analyses of Critical Behavior

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.

arXiv comment17 pagess 10 figures

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• Conservation Laws and Spin System Modeling through Principal Component Analysis
• A Projected Entropy Controller for Transition Matrix Calculations
• A Cluster Controller for Transition Matrix Calculations
• Accuracy and Efficiency of Simplified Tensor Network Codes
• Transition Matrix Cluster Algorithms