Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation

Abstract

A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity C are derived from derivatives of the partition function. We also derive a formula for the exchange probability in the replica exchange Monte Carlo method. By combining the formulae with the Stochastic Cutoff method, we can greatly reduce the computational time to perform internal energy and heat capacity measurements and the replica exchange Monte Carlo method in long-range interacting systems. Numerical simulations in three dimensional magnetic dipolar systems show the validity and efficiency of the method.

11 pages, 6 figures, to appear in PRE

References in corpus (4)

• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Stochastic Cutoff Method for Long-Range Interacting Systems
• A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms
• Peculiar from-Edge-to-Interior Spin Freezing in a Magnetic Dipolar Cube

Cited by in corpus (3)

• Study on Effects of Dipole-dipole Interactions in Nd_2Fe_{14}B thin film Based on Stochastic Cut-off Method with New Efficient Algorithm
• An Efficient Monte-Carlo Method for Calculating Free-Energy in Long-Range Interacting Systems
• Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems