Figure 4

Dynamics of the Wang-Landau algorithm. Typical time evolution of the histogram of visited states when starting with different initial guesses. The model parameters are RQGS with L _Q = L _S = 348. The weights have been updated dynamically with modification factor ϕ = exp(0.1) ≈ 1.105. (a) w(s) = 1 for all s. The Markov chain converges relatively slowly. (b) w(s) ≈ 1/Prob(S = s|L _Q = 348, L _S = 200) has been used as an initial guess. The histogram becomes flatter within remarkable less computational effort. Inset: a detailed balance simulation (ϕ = 1 during the simulation of 1, 048, 576 steps) with initial weights that are close to the inverse target distribution. Though the histograms are not "flat", each score value on the interval [23, 500] has been visited. The estimate from this data can be used in a longer production run.