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Journal of Physics A Mathematical and General

A renormalisation group technique for spin and gauge systems with topological excitations

Gerardo Aldazabal, Néstor Parga

Published May 1, 1982• 0 citations
Publisher

Abstract

The authors' present a real space renormalisation group technique able to deal explicitly with gases of topological excitations. As examples they consider the two-dimensional XY model and the three-dimensional compact electrodynamics.
DOI
10.1088/0305-4470/15/5/025

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The central charge of the Virasoro algebra of the one-dimensional dimerised XY model with arbitrary boundary conditions is obtained at criticality. The authors obtain c=1-12 tau 2 where tau (0<or= tau <or=1/2) characterises the boundary conditions. This shift of c yields relations between the XY model and both the q-state Potts model and the O(N) model. They show that the phenomenological renormalisation group equation, which is used to estimate the critical value of the parameter of the system, has no real solution for the range tau >1/26. This corresponds to the non-unitary Potts model (0<or=q<2) and the O(N) one (-2<or=N<1).