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Percolation on the average and spontaneous magnetization for q-states Potts model on graph

Alessandro Vezzani
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Abstract

We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over all the sites of the graph the probability of belonging to a cluster of a given size. In the paper we obtain an inequality between this average probability and the average magnetization, which is a typical extensive function describing the thermodynamic behaviour of the model.

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Alessandro Vezzani. 2005-02-08. Percolation on the average and spontaneous magnetization for q-states Potts model on graph. https://doi.org/10.1088/0305-4470%2F37%2F1%2F005

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