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We considered a higher-dimensional extension for the replica-exchangeWang-Landau algorithm to perform a random walk in the energy and magnetizationspace of the two-dimensional Ising model. This hybrid scheme combines theadvantages of Wang-Landau and Replica-Exchange algorithms, and theone-dimensional version of this approach has been shown to be very efficientand to scale well, up to several thousands of computing cores. This approachallows us to split the parameter space of the system to be simulated intoseveral pieces and still perform a random walk over the entire parameter range,ensuring the ergodicity of the simulation. Previous work, in which a similarscheme of parallel simulation was implemented without using replica exchangeand with a different way to combine the result from the pieces, led todiscontinuities in the final density of states over the entire range ofparameters. From our simulations, it appears that the replica-exchangeWang-Landau algorithm is able to overcome this difficulty, allowing explorationof higher parameter phase space by keeping track of the joint density ofstates.

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space