title: Inverse Mermin-Wagner theorem for classical spin models on graphs.
abstract: In this paper we present the inversion of the Mermin-Wagner theorem on graphs, by proving the existence of spontaneous magnetization at finite temperature for classical spin models on transient on the average graphs, i.e., graphs where a random walker returns to its starting point with an average probability F<1. This result, which is here proven for models with O(n) symmetry, includes as a particular case n=1, providing a very general condition for spontaneous symmetry breaking on inhomogeneous structures even for the Ising model.
authors.affiliation: Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica, Università di Parma, Parco Area delle Scienze n. 7A, 43100 Parma, Italy. burioni@pr.infn.it
authors.forename: R
authors.initials: R
authors.lastname: Burioni
authors.forename: D
authors.initials: D
authors.lastname: Cassi
authors.forename: A
authors.initials: A
authors.lastname: Vezzani