Mean-field (n,m)-cluster approximation for lattice models

We introduce and study an implementation technique of the mean-field dynamic-cluster method for the analysis of lattice models. The technique is characterized by two indices (n,m), where n is the size of the clusters and m denotes their overlap. For some lattice models, we find that the cluster method converges to the exact kinetics with increasing cluster size n, in a conventional way. However, for some other models it is shown that the cluster approximation predicts a phase diagram that is qualitatively incorrect even for large n. A reason for this anomalous behavior is suggested. The effect of different, but physically equivalent, representations of the same lattice model on the quality of the approximation results is also explored.