Reformulation of the stochastic potential switching algorithm and a generalized Fourtuin-Kasteleyn representation

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 formulas 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 of the method.