Optimized multicanonical simulations: a new proposal based on classical fluctuation theory

Abstract

We propose a new recursive procedure to estimate the microcanonical density of states in multicanonical Monte Carlo simulations which relies only on measurements of moments of the energy distribution, avoiding entirely the need for energy histograms. This method yields directly a piecewise analytical approximation to the microcanonical inverse temperature, $\beta (E)$, and allows improved control over the statistics and efficiency of the simulations. We demonstrate its utility in connection with recently proposed schemes for improving the efficiency of multicanonical sampling, either with adjustment of the asymptotic energy distribution or with the replacement of single spin flip dynamics with collective updates.

8 pages, 10 figures

References in corpus (5)

• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Exact Solution of Ising Model on a Small-World Network
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Cited by in corpus (4)

• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Doubly degenerate orbital system in honeycomb lattice: implication of orbital state in layered iron oxide
• Wang-Landau/Multibondic Cluster Simulations for Second-Order Phase Transitions
• Projected single-spin flip dynamics in the Ising Model