Mathematics Colloquia and Seminars

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I will present a novel approach to the study of complex zeros of partition functions of lattice statistical mechanics (i.e., moment generating functions of the Hamiltonian of a spin system on a lattice). Using the Pirogov-Sinai theory, which typically requires that the temperature is very low, the roots of the partition function of a spin system in, say, a complex magnetic field and a box with periodic boundary condition can be localized up to an error exponentially small in the size of the box. Under appropriate non-degeneracy conditions, the roots condensate on curves (as the size of the box tends to infinity) of the complex-field phase diagram.