English

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

Statistical Mechanics 2009-11-10 v2

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.

Keywords

Cite

@article{arxiv.cond-mat/0306167,
  title  = {Percolation on the average and spontaneous magnetization for q-states Potts model on graph},
  author = {Alessandro Vezzani},
  journal= {arXiv preprint arXiv:cond-mat/0306167},
  year   = {2009}
}