Limit cycles in the BCS and the sine-Gordon models

by Sierra, German

Abstract

Wilson suggested in 1971 the possibility that a renormalization group flow could end not on isolated fixed points but on limit cycles. This possibility has been recently realized in a variety of systems, particularly in a modified version of the BCS model of superconductivity which posseses an infinite number of condensates characterized by a "russian doll" scaling and in the sine-Gordon model in the "crossover regime", where the Kosterlitz-Thouless RG flow can be extended analytically through infinity. The conjectured S-matrix theory of the cyclic sine-Gordon model has an infinite number of resonances with a "russian doll" scaling.