Phase transitions in the uniformly frustrated XY model with frustration parameter f=1/3 studied with use of the microcanonical Monte Carlo technique.

Abstract

We study the phase transition of the frustrated XY model in the square lattice with frustration f=1/3. The system has a discrete ${\mathit{Z}}_{3}$\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ symmetry and a continuous U(1) symmetry. We study the system via the microcanonical Monte Carlo technique. We have found that the system has three kinds of phase transitions. At the temperature 0.208J/${\mathit{k}}_{\mathit{B}}$, the system has a Kosterlitz-Thouless transition with a larger-than-universal jump in the helicity modulus. At the temperature 0.215J/${\mathit{k}}_{\mathit{B}}$, the system has a vortex-lattice melting transition related to discrete ${\mathit{Z}}_{2}$ symmetry. At some higher temperature 0.219J/${\mathit{k}}_{\mathit{B}}$, the system has a second-order vortex-lattice melting transition related to ${\mathit{Z}}_{3}$ symmetry. It is also found that the second transition gives a weak anomaly of the specific heat while the third transition gives rise to the divergence in the specific heat.