Geometric cluster Monte Carlo simulation

We discuss a cluster Monte Carlo algorithm for lattice models, based on geometric transformations. We prove detailed balance when the transformation is self-inverse, and a symmetry of the Hamiltonian. This algorithm opens new possibilities, in particular for the efficient simulation of critical model systems, where the Metropolis method suffers from critical slowing down. We illustrate the generality of our method by applications to the Ising model in the constant-magnetization ensemble, and to the tricritical Blume-Capel model.