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Cluster Percolation and Explicit Symmetry Breaking in Spin Models

Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n), etc., can be equivalently described as a percolation transition of clusters. We study here the behaviour of such clusters when the presence of an external field H breaks explicitly the global symmetry of the Hamiltonian of the theory. We find that these clusters have still some interesting relationships with thermal features of the model.