Wang–Landau sampling: Saving CPU time

Abstract

In this work we propose an improvement to the Wang–Landau (WL) method that allows an economy in CPU time of about 60% leading to the same results with the same accuracy. We used the 2D Ising model to show that one can initiate all WL simulations using the outputs of an advanced WL level from a previous simulation. We showed that up to the seventh WL level (f6) the simulations are not biased yet and can proceed to any value that the simulation from the very beginning would reach. As a result the initial WL levels can be simulated just once. It was also observed that the saving in CPU time is larger for larger lattice sizes, exactly where the computational cost is considerable. We carried out high-resolution simulations beginning initially from the first WL level (f0) and another beginning from the eighth WL level (f7) using all the data at the end of the previous level and showed that the results for the critical temperature Tc and the critical static exponents β and γ coincide within the error bars. Finally we applied the same procedure to the 1/2-spin Baxter–Wu model and the economy in CPU time was of about 64%.