Monte Carlo simulation of spin models with long-range interactions

An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions between this spin and the other spins in the system. In addition, critical slowing down is strongly suppressed. In order to illustrate the range of applicability of the algorithm, two specific examples are presented. First, some aspects of the Kosterlitz-Thouless transition in the one-dimensional Ising chain with inverse-square interactions are calculated. Secondly, the crossover from Ising-like to classical critical behavior in two-dimensional systems is studied for several different interaction profiles.