Multibondic cluster algorithm for finite-size scaling studies of critical phenomena

For finite-size scaling studies of second-order phase transitions the critical energy range of interest is usually larger than the energy range covered by a canonical Monte Carlo simulation close to the critical temperature. The desired extended energy range can be covered, in principle, by performing a Wang–Landau recursion for the density of states followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. We show that a cluster version of the Wang–Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficacy of the conventional approach by power laws in the lattice size. By using finite-size scaling theory for suitably adapting the extended energy range to the system size, in our simulations real gains in CPU time reach two orders of magnitude.