A two-dimensional (2D) fully frustrated
XY (FFXY) class of models is shown to contain a different ground state in addition to the checkerboard ground states of the standard 2D
FFXY 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
Z2 Ising-type transitions. This suggests that the class of 2D
FFXY 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
FFXY model are discussed in particular with respect to the long-standing controversy concerning the characteristics of its phase transitions.
We study the phase diagram and critical behaviour of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau–Ginzburg–Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on L × L square lattices, up to L = O (10 3 ). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz–Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models, in a rather large parameter region, show a crossover behaviour at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behaviour is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behaviour of the 4-vector model.
We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L , L ≲ 10 3 . We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.
The issue of the number, nature and sequence of phase transitions in the fully frustrated XY (FFXY) model is a highly non trivial one due to the complex interplay between its continuous and discrete degrees of freedom. In this contribution we attack such a problem by means of a twisted conformal field theory (CFT) approach and show how it gives rise to the U (1)
⊗Z2 symmetry and to the whole spectrum of excitations of the FFXY model.
Following an earlier suggestion, we show how the symmetry of the fully frustrated XY ( FFXY ) model on a square lattice can be accounted for in the framework of the m -reduction procedure developed for a Quantum Hall system at 'paired states' fillings ν = 1. The resulting twisted conformal field theory (CFT) with central charge c = 2 is shown to well describe the physical properties of the FFXY model. In particular, the whole phase diagram is recovered by analysing the flow from the Z 2 degenerate vacuum of the c = 2 CFT to the infrared fixed point unique vacuum of the CFT. The last theory is known to successfully describe the critical behaviour of the system at the overlap temperature for the Ising and vortex-unbinding transitions.
We investigate a 19-vertex version of the two-dimensional fully frustrated XY (FFXY) model. We construct Yang-Baxter equations for this model and show that there is no solution. Therefore we have chosen a numerical approach based on the transfer matrix. The results show that a coupled XY Ising model is in the same universality class as the FFXY model. We find that the phase coupling over an Ising wall is irrelevant at criticality. This leads to a correction of earlier determinations of the dimension
xh,Is∗ of the Ising disorder operator. We find
xh,Is∗=0.123(5) and a conformal anomaly c=1.55(5). These results are consistent with the hypothesis that the FFXY model behaves as a superposition of an Ising model and an XY model. However, the dimensions associated with the energy,
xt=0.77(3), and with the XY magnetization
xh,XY\ensuremath{\approxeq}0.17, refute this hypothesis.