A Model with Simultaneous First and Second Order Phase Transitions

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We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two “bond ordered phases”, one with local ferromagnetic order and another with local anti-ferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen [1]. This last result generalizes the result of van Enter and Shlosman [2] We argue that these phenomena are quite general and should occur for a large class of potentials.

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