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

TL;DR

This paper introduces a reformulated stochastic potential switching algorithm that leads to a generalized Fortuin-Kasteleyn representation, enabling more efficient computation of thermodynamic quantities and replica exchange in long-range systems.

Contribution

The paper presents a new formulation of the stochastic potential switching algorithm and derives generalized formulas for partition function, internal energy, heat capacity, and exchange probability.

Findings

Validates the method with numerical simulations on 3D magnetic dipolar systems.

Demonstrates significant reduction in computational time.

Shows improved efficiency in long-range interacting systems.

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.