Equilibrium times for the Multicanonical Method

This work measures the time to equilibrium for the multicanonical method on the 2DIsing system by using a new criterion, proposed here, to find the time to equilibrium, teq, of any sampling procedure based on a Markov process. Our new procedure gives the same results that the usual one, based on the magnetization, for the canonical Metropolis sampling on a 2D-Ising model at several temperatures. For the multicanonical method we found a power-law relationship with the system size, L, of teq=0.27(15)L and with the number of energy levels to explore, kE, of teq=0.7(13)k 1.40(11) E , in perfect agreement with the result just above. In addition, a kind of critical slowing down was observed around the critical energy. Our new procedure is completely general, and can be applied to any sampling method based on Markov processes.