Topological transitions in two-dimensional lattice spin models.

A family of classical statistical-mechanical spin models, by now extensively studied in the literature, involves two-component unit vectors, associated with a two-dimensional lattice, with pair potentials restricted to nearest neighbors and possessing 0(2) symmetry--i.e., defined by some function of the scalar product between the two interacting spins; these studies often show the existence of a topological phase transition. We show here that, for a wide class of interaction models of the above type, available mathematical results entail the existence of a topological (Berezinskiĭ-Kosterlitz-Thouless-like) transition, as well as a rigorous lower bound on the transition temperature.