Cluster Monte Carlo: Extending the range

Monte Carlo simulations with local updates tend to become time-consuming when large-scale correlations exist, such as in critical systems. For a limited, but increasing number of model systems, nonlocal 'cluster' algorithms are available that are orders of magnitude more efficient than algorithms with local updates. Cluster algorithms can be defined on the basis of the symmetry properties of the Hamiltonian; different symmetries can thus lead to different cluster algorithms. We review a number of existing cluster algorithms, and describe new ones for an Ising-like model with two- and three-spin interactions, and for the chiral Potts model. New simulation data for the Ising-like model allow an accurate determination of its specific-heat exponent; this result confirms existing ideas that the model belongs to the 4-state Potts universality class.