Renormalization-group analysis of a class of two-dimensional vortex systems

Abstract

The statistical-mechanical properties of a class of two-dimensional vortex systems, described by grand-canonical partition functions containing certain Z n- valued adiabatic phases, are investigated. It has been shown previously that such systems describe two-dimensional incompressible superfluids, in which an additional (non-thermal) vortex is present, and which is restricted to move along a closed curve enclosing the bulk fluid. By generalizing the well-known connection between the Coulomb-gas partition function and the two-dimensional sine-Gordon model, to include adiabatic phases, we derive a series of renormalization-group equations, the asymptotic solutions of which determined the macroscopic superfluid density. Numerical solutions to these equations are given, from which it is concluded that although the density is discontinuous along a line of critical temperatures T c, the size of the discontinuity is reduced by a factor of 1/ n compared to the case where adiabatic phases are absent.