Percolation on the average and spontaneous magnetization for q-states Potts model on graph
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 this 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- January 2004
- DOI:
- 10.1088/0305-4470/37/1/005
- arXiv:
- arXiv:cond-mat/0306167
- Bibcode:
- 2004JPhA...37...77V
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- J. Phys. A 37 (2004) 77-83