Inverse Mermin-Wagner theorem for classical spin models on graphs.
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.
Burioni
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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
Cassi
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Vezzani
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