The Isinglike phase transition in the square lattice fully frustrated XY model with nearest next neighbor (NNN) couplings is studied using the finitesize scaling theory. The critical temperature Tc and static critical exponents 2β/ν and ν are determined. When the NNN coupling variable x=0.5, it is found that in the model exists Isinglike phase transition with the critical temperature Tc=0.404 3±0.000 5 and ν= 0.80±0.05.
The Isinglike phase transition in the square lattice fully frustrated XY model with nearest next neighbor (NNN) couplings is studied using the finitesize scaling theory. The critical temperature Tc and static critical exponents 2β/ν and ν are determined. When the NNN coupling variable x=0.5, it is found that in the model exists Isinglike phase transition with the critical temperature Tc=0.404 3±0.000 5 and ν= 0.80±0.05.
The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated XY model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings is investigated using Monte Carlo simulations. When x<1/2(x is the ratio between NNN and NN couplings), the transition temperature Tc and the dynamic and static critical exponents z, $2\ensuremath{\beta}/\ensuremath{\nu},$ and $\ensuremath{\nu}$ are estimated using the short-time dynamic scaling analysis. Except x close to the critical value 1/2, the critical exponents $2\ensuremath{\beta}/\ensuremath{\nu}$ and $\ensuremath{\nu}$ are found to be almost independent of the NNN coupling, indicating that the second-order phase transitions in the FFXY model, with or without NNN coupling, are in the same universality class. When x>1/2, the short-time dynamic study suggests that there is no second-order phase transition, in agreement with the previous result [Phys. Rev. B 62, R9287 (2000)].
Phase transitions and critical properties of the frustrated Ising model on a cubic lattice with next-nearest-neighbor intralayer interactions are investigated by the replica Monte Carlo method. Estimations are made for the magnitude relation of the next-nearest-neighbor and nearest-neighbor exchange interactions r = J2/J1 in the value ranges of r ∈ [0.0, 1.0]. The phase diagram of the dependence of critical temperature on the next-nearest-neighbor interaction has been plotted. The static critical exponents of the heat capacity, the susceptibility, the ordering parameter and the correlation length as well as the Fisher exponent are calculated by means of the finite-size scaling theory. The universality class of the critical behavior of this model is revealed to remain within the limits of values r ∈ [0.0, 0.4]. It is found that the change in the next-nearest-neighbor interaction value in the range of r ∈ [0.9, 1.0] leads to another critical behavior.
Phase transitions and critical characteristics of the layered antiferromagnetic Ising model in the case of a cubic lattice with next-nearest-neighbor intralayer interactions are studied in the framework of the Monte Carlo method implementing the replica algorithm. The characteristics of the phase transitions are analyzed within the histogram method and with the Binder cumulants. For the model under study, it is found that the transition from the superantiferromagnetic phase to the paramagnetic one is a second order phase transition. The static critical exponents for the specific heat α, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent η are calculated using the finite-size scaling theory. It is shown that the three-dimensional Ising model for the cubic lattice with next-nearest-neighbor interactions belongs to the same universality class of critical behavior as the completely frustrated three-dimensional Ising model.
We study the critical behavior of the fully frustrated XY model on a square lattice by means of extensive histogram Monte Carlo simulations. We find a single transition in contrast to the scenario of two distinct transitions. From a finite-size scaling we determine the critical exponents associated with the Ising-like order parameter and find ${T}_{c}(\ensuremath{\infty})=0.4552(2)$, $\ensuremath{\nu}=0.852(2),$ and $\ensuremath{\gamma}=1.531(3)$. These exponents, different from the pure two-dimensional Ising critical exponents, are in agreement with the ones obtained for a mixed XY Ising system.
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 obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent nu. Our results are compared to previous results for this system using a wide variety of other approaches.