The Ising-like phase transition of the two-dimensional fully frustrated XY model with weak positional disorder is studied in a short-time dynamic-scaling scheme. It is observed that the weak disorder does not destroy the Ising-like order. Besides the critical temperature, all the static and dynamic critical exponents are estimated.
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)].
Short-time dynamic behaviour of two-dimensional fully frustrated XY model near the Ising-like phase-transition temperature is studied with resistively shunted junction dynamics. The transition temperature T c and the dynamic and static critical exponents z , 2β/ν and ν are estimated under both a periodic boundary condition (PBC) and a fluctuating twist boundary condition (FTBC) using the short-time dynamic scaling analysis. The results show that T c , 2β/ν and ν are almost independent of the boundary conditions, whereas z depends on the boundary condition. The value of z = 2.18(5) of the PBC is roughly equal to that of the FF XY model with Monte Carlo dynamics under the PBC, while z = 2.05(4) of the FTBC is in agreement with that of the Coulomb gas model.
Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature Tc and all the dynamic and static critical exponents $\ensuremath{\theta}$, z, $\ensuremath{\beta}$, and $\ensuremath{\nu}$.
We investigate the influence of the boundary condition on the short-time dynamic behaviour of the Ising-like phase transition in square-lattice fully frustrated (FF) XY models with periodic and fluctuating twist boundary conditions. The transition temperature T c and the dynamic and static critical exponents z , 2β/ν and ν are estimated for both cases using short-time dynamic scaling analysis. The results show that both models have the same critical exponents, indicating that the boundary condition has nearly no effect on the short-time dynamic behaviour of the FF XY 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.