Phase transitions in uniformly frustratedXYmodels

Abstract

We develop the Hubbard-Stratanovich transform for uniformly frustrated XY models both on a square lattice and on a triangular lattice, and construct the Landau-Ginzburg-Wilson Hamiltonians, which reflect the formation of various superlattices according to values of the frustration f. Near the critical point the system f=(1/4) on a triangular lattice is shown to belong to the same universality class as the fully frustrated (f=(1/2)) system on a square lattice. By decomposing two-mode systems into two coupled XY models and by applying the Migdal-Kadanoff approximation, we show the possibility of Ising-like or three-state Potts-like transitions in addition to the Kosterlitz-Thouless–like ones.