Monte Carlo study of the Coulomb-gas representation of frustrated XY models.

Abstract

We construct a model consisting of a half-integer Coulomb gas, corresponding to the frustrated XY model, and add an Ising interaction J to it. In this system, it is possible to vary the Coulomb interaction strength, corresponding to the vortex interaction in the frustrated model, separately from the Ising interaction of the domain walls. The model is studied theoretically and numerically to obtain the phase diagram. We observe at high J values two critical lines. One corresponds to an Ising transition, the other to a Kosterlitz-Thouless transition with a jump in the helicity modulus (inverse dielectric constant) in accordance with the universal value to be expected for unit charges. At J=0 the two critical branches coincide (as has been found in direct Monte Carlo simulations) to a single critical line for J\ensuremath{\le}0 which has both Ising and Kosterlitz-Thouless critical characteristics. However, the jump in the helicity modulus no longer appears to be universal further down this line.