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Renormalization Transformations in the Vicinity of First-Order Phase Transitions: What Can and Cannot Go Wrong

By Aernout C.D. van Enter, Roberto Fernández and Alan D. Sokal


We reconsider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the other hand, we prove in several cases that near a first-order phase transition the renormalized measure is not a Gibbs measure for any reasonable interaction. It follows that the conventional RG description of first-order transitions is not universally valid

Year: 1991
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Provided by: NARCIS
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