Wang–Landau multibondic cluster approach to simulations of second-order transitions

At second-order phase transitions the critical energy range covered by a canonical Monte Carlo simulation close to the critical temperature is often smaller than the energy range needed for reliable reweighting analyses of certain observables. Such an extended energy range can be covered by performing a Wang–Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach based on local update rules one loses the advantage due to non-local cluster algorithms which are well known to drastically reduce critical slowing down. We develop a cluster version of the Wang–Landau recursion together with a subsequent multibondic simulation and show for 2D and 3D Ising models that the efficiency of the conventional Wang–Landau multicanonical approach can be improved by power laws in the lattice size. In our simulations real gains in CPU time reach two orders of magnitude.