We consider the 2D J 1 − J 2 classical XY model on a square lattice. In the frustrated phase corresponding to J 2 > J 1 /2, an Ising order parameter emerges by an "order due to disorder" effect. This leads to a discrete symmetry plus the O (2) global one. We formulate the problem in a Coulomb gas language and show by a renormalization group analysis that only two phases are still possible: a locked phase at low temperature and a disordered one at high temperature. The transition is characterized by the loss of Ising and XY order at the same point. This analysis suggests that the 2D J 1 − J 2 XY model is in the same universality class as XY-Ising models.
We consider the 2D J 1 − J 2 classical XY model on a square lattice. In the frustrated phase corresponding to J 2 > J 1 /2, an Ising order parameter emerges by an "order due to disorder" effect. This leads to a discrete symmetry plus the O (2) global one. We formulate the problem in a Coulomb gas language and show by a renormalization group analysis that only two phases are still possible: a locked phase at low temperature and a disordered one at high temperature. The transition is characterized by the loss of Ising and XY order at the same point. This analysis suggests that the 2D J 1 − J 2 XY model is in the same universality class as XY-Ising models.
We consider the two-dimensional (2D) ${J}_{1}\ensuremath{-}{J}_{2}$ classical XY model on a square lattice. In the frustrated phase corresponding to J2>J1/2, an Ising-like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete Z2 symmetry plus the U(1) global one. Using a powerful algorithm we show that the system undergoes two transitions at different but still very close temperatures, one of Kosterlitz-Thouless (KT) type and another one which does not belong to the expected Ising universality class. A new analysis of the KT transition has been developed in order to avoid the use of the nonuniversal helicity jump and to allow the computation of the exponents without a precise determination of the critical temperature. Moreover, our huge number of data enables us to exhibit the existence of large finite size effects explaining the dispersed results found in the literature concerning the more studied frustrated 2D, XY models.
We investigate the XY model with ferromagnetic nearest and antiferromagnetic next-to-nearest neighbours couplings (ANNNXY model). We formulate the study of both phases of the model in terms of different Coulomb gas models. The non-frustrated ferromagnetic phase is thus transformed into a usual Coulomb gas with one species, whereas the frustrated phase is translated into a Coulomb gas with three species interacting with each other in an anisotropic lattice. We then generalize the Kosterlitz - Thouless renormalization group equations for both phases by treating the Ising and Kosterlitz - Thouless order parameters in an independent way. This enables us to discuss the nature of the transition (Ising and (or) Kosterlitz - Thouless) in the frustrated phase.
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 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.
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 investigate the finite-temperature phase diagram of the classical ${J}_{1}\ensuremath{-}{J}_{2}$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and next-to-nearest-neighbor interactions, exhibits a complex interplay between U(1) and Z2 symmetries. Our study reveals an emergent intermediate phase around ${J}_{2}/{J}_{1}\ensuremath{\sim}0.505$, which is characterized by a Z2 long-range stripe order without phase coherence in the XY spins. The intermediate phase features two well-separated phase transitions: a higher-temperature Ising transition and a lower-temperature Berezinskii-Kosterlitz-Thouless (BKT) transition. The relative separation between these transitions is significantly larger than previously reported, enabling a clearer investigation of their distinct thermodynamic properties. For 0.5<J2/J1<0.501, two transitions merge into a single first-order phase transition, a phenomenon that cannot be explained solely by mapping to the Ising-XY model. As ${J}_{2}/{J}_{1}\ensuremath{\rightarrow}\ensuremath{\infty}$, the transition evolves continuously into the BKT universality class. These findings advance the understanding of the mechanisms driving phase transitions in frustrated spin systems, and they suggest potential experimental realizations in platforms such as ultracold atoms, Josephson junction arrays, and optical lattices.