Symmetry-allowed phase transitions realized by the two-dimensional fully frustratedXYclass

Abstract

A two-dimensional (2D) fully frustrated $XY$ $(\text{FF}XY)$ class of models is shown to contain a different ground state in addition to the checkerboard ground states of the standard 2D $\text{FF}XY$ model. The spin configuration of this additional ground state is obtained. Associated with this ground state there are additional phase transitions. An order parameter accounting for these transitions is proposed. The transitions associated with this order parameter are suggested to be similar to a 2D liquid-gas transition which implies ${Z}_{2}$ Ising-type transitions. This suggests that the class of 2D $\text{FF}XY$ models belongs within a $U(1)\ensuremath{\bigotimes}{Z}_{2}\ensuremath{\bigotimes}{Z}_{2}$ designation of possible transitions, which implies that there are seven different possible single and combined transitions. Monte Carlo (MC) simulations for the generalized fully frustrated $XY$ model on a square lattice are used to investigate which of these possibilities can be realized in practice: five of the seven are encountered. Four critical points are deduced from the MC simulations: three are consistent with central charge $c=3/2$ and one is consistent with $c=1$. The implications for the standard 2D $\text{FF}XY$ model are discussed in particular with respect to the long-standing controversy concerning the characteristics of its phase transitions.