ABSTRACT
We propose a recursive procedure to estimate the microcanonical density of states in multicanonical Monte Carlo simulations which relies only on measurements of moments of the energy distribution, avoiding entirely the need for energy histograms. This method yields directly a piecewise analytical approximation to the microcanonical inverse temperature beta(E) and allows improved control over the statistics and efficiency of the simulations. We demonstrate its utility in connection with recently proposed schemes for improving the efficiency of multicanonical sampling, either with adjustment of the asymptotic energy distribution or with the replacement of single spin flip dynamics with collective updates.
ABSTRACT
We present an exact solution of a one-dimensional Ising chain with both nearest-neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean-field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.