GEOMETRIC CLUSTER MONTE-CARLO SIMULATION

We discuss a cluster Monte Carlo algorithm for lattice models, based o n geometric transformations. We prove detailed balance when the transf ormation is self-inverse, and a symmetry of the Hamiltonian. This algo rithm opens new possibilities, in particular for the efficient simulat ion of critical model systems, where the Metropolis method suffers fro m critical slowing down. We illustrate the generality of our method by applications to the Ising model in the constant-magnetization ensembl e, and to the tricritical Blume-Capel model.