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

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

2003-06-06

arxiv.org/abs/cond-mat/0306167v2

J. Phys. A 37 (2004) 77-83

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/0305-4470/37/1/005

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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