GEOMETRIC SYMMETRIES AND CLUSTER SIMULATIONS

Cluster Monte Carlo methods are especially useful for applications in the vicinity of phase transitions, because they suppress critical slow ing down; this may reduce the required simulation times by orders of m agnitude. In general, the way in which cluster methods work can be exp lained in terms of global symmetry properties of the simulated model. In the case of the Swendsen-Wang and related algorithms for the Ising model, this symmetry is the plus-minus spin symmetry; therefore, these methods are not directly applicable in the presence of a magnetic fie ld. More generally, in the case of the Potts model, the Swendsen-Wang algorithm relies on the permutation symmetry of the Potts states. Howe ver, other symmetry properties can also be employed for the formulatio n of cluster algorithms. Besides of the spin symmetries, one can use g eometric symmetries of the lattice carrying the spins. Thus, new clust er simulation methods are realized for a number of models. This geomet ric method enables the investigation of models that have thus far rema ined outside the reach of cluster algorithms. Here, we present some si mulation results for lattice gases, and for an Ising model at constant magnetization. This cluster method is also applicable to the Blume-Ca pel model, including its tricritical point. (C) 1998 Elsevier Science B.V. All rights reserved.