Discrete Random Walks, DRW'03
Cyril Banderier and Christian Krattenthaler (eds.)
DMTCS Conference Volume AC (2003), pp. 333344
author:  Alessandro Vezzani, Davide Cassi and Raffaella Burioni 

title:  Average properties of combinatorial problems and thermodynamics of spin models on graphs 
keywords:  statistical mechanics, graphs, randomwalks, percolation 
abstract: 
The study of thermodynamic properties of classical spin
models on infinite graphs naturally leads to consider the
new combinatorial problems of randomwalks and percolation
on the average. Indeed, spin models with
O(n)
continuous symmetry present spontaneous magnetization
only on transient on the average graphs, while models with
discrete symmetry (Ising and Potts) are spontaneously
magnetized on graphs exhibiting percolation on the average.
In this paper we define the combinatorial problems on the
average, showing that they give rise to classifications of
graph topology which are different from the ones obtained
in usual (local) randomwalks and percolation. Furthermore,
we illustrate the theorem proving the correspondence
between Potts model and average percolation.

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reference:  Alessandro Vezzani and Davide Cassi and Raffaella Burioni (2003), Average properties of combinatorial problems and thermodynamics of spin models on graphs, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 333344 
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