06-279 Rafael de la Llave, Enrico Valdinoci

Ground states and critical points for Aubry-Mather theory in statistical mechanics (526K, PostScript) Oct 4, 06

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Abstract. We consider statistical mechanics systems that are defined on a set with some symmetry properties. Each of the sites has a real order parameter. We assume that the interaction is ferromagnetic as well as symmetric with respect to the action of a group which is assumed to be finitely generated and residually finite. Given any cocycle of the symmetry group, we prove that there are ground states which satisfy an order condition (known as Birkhoff property) and that are at a bounded distance to the cocycle. Such ground states are organized into a (possibly singular) lamination. Furthermore, we show that, given any completely irrational cocycle, either the above lamination consists of a foliation made of a continuous one parameter family of ground states, or, inside any gap of the lamination, there is a well-ordered critical point which is not a ground state.

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