Abstract
Recently Pirogov and Sinai developped a theory of phase transitions in systems satisfying Peierls condition. We give a criterium for the Peierls condition to hold and apply it to several systems. In particular we prove that ferromagnetic system satisfies the Peierls condition iff its (internal) symmetry group is finite. And using an algebraic argument we show that in two dimensions the symmetry groups of reduced translation invariant systems is finite.
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