New Implementations of Replica-exchange Method for Simulations of Complex Systems: Designed-walk and Deterministic Replica-exchange Methods

Two new methods of replica-exchange method (REM) are tested for a two-dimensional Ising spin model. The first method is the deterministic replica-exchange method (DETREM) which uses a differential equation based on Gibbs sampling method instead of Metropolis criteria. The other is the designed-walk replica-exchange method (DEWREM) which determines the trajectory of replica in temperature space without random walk. This method gives more number of tunneling events than conventional REM, where the tunneling event is a round-trip of temperature from the lowest to the highest back to the lowest. We examined physical quantities such as magnetization and susceptibility. Our new methods reproduced the results of the conventional random-walk REM.