TY - JOUR
T1 - Regularity properties and pathologies of position-space renormalization-group transformations
AU - van Enter, Aernout C.D.
AU - Fernández, Roberto
AU - Sokal, Alan D.
PY - 1991/5/20
Y1 - 1991/5/20
N2 - We consider 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.
AB - We consider 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.
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U2 - 10.1016/0920-5632(91)90880-N
DO - 10.1016/0920-5632(91)90880-N
M3 - Article
AN - SCOPUS:0010694020
SN - 0920-5632
VL - 20
SP - 48
EP - 52
JO - Nuclear Physics B (Proceedings Supplements)
JF - Nuclear Physics B (Proceedings Supplements)
IS - C
ER -