Intrinsic convergence properties of entropic sampling algorithms

We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang?Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f???f/2) each time the flat-histogram condition is satisfied, in the second f???1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E?=?1, ..., L, there is exactly one state, that is, g(E)?=?1 for all E. Convergence of sampling corresponds to g(E, t)???const. as t????, so that the standard deviation ?g of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases ?g saturates at long times. In the 1/t algorithm, by contrast, ?g decays . Modified TS and 1/t procedures, in which f???1/t?, converge for ? values between 0? 1 the initial error is never completely eliminated.