Phase diagram of the frustrated XY model on a triangular lattice.

Abstract

We formulate a Coulomb gas (CG) model consisting of fractional charges \ifmmode\pm\else\textpm\fi{}(1/2 on a honeycomb lattice, representing a frustrated XY model on a triangular lattice. An Ising interaction with coupling constant J is added to this Coulomb gas so as to be able to vary the Ising domain-wall energy independently from the Coulomb gas coupling K. In this model, we find Kosterlitz-Thouless and Ising transitions at separate temperatures for positive J. The point in the phase diagram of this model where the Ising and Kosterlitz-Thouless transition lines meet, has negative J, in contrast to a similar model on a square lattice, that was studied in previous paper, where the transition lines merge at J=0, corresponding to the ``pure'' frustrated XY model. For larger K values (and more negative J), both transitions continue as a single line. Arguments have been given for this line to bifurcate again in the honeycomb CG at very large K. This was not observed, as the system switches over to a different ground state, thus inducing a first-order transition.