Broad histogram relation for the bond number and its applications
Chiaki Yamaguchi, Naoki Kawashima, and Yutaka Okabe
TL;DR
This paper introduces a new Monte Carlo method based on a broad histogram relation for the bond number in spin models, improving the calculation of the density of states and physical quantities.
Contribution
It derives a rigorous broad histogram relation for the bond number and proposes a Monte Carlo dynamics utilizing this relation, enhancing computational efficiency.
Findings
Efficient calculation of the density of states using BHR for bond number
Demonstrated improved accuracy in physical quantity estimation
Validated the method's effectiveness through simulations
Abstract
We discuss Monte Carlo methods based on the cluster (graph) representation for spin models. We derive a rigorous broad histogram relation (BHR) for the bond number; a counterpart for the energy was derived by Oliveira previously. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed. We show the efficiency of the BHR for the bond number in calculating the density of states and other physical quantities.
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