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Chinese Physics Letters

Influence of the Boundary Condition on the Short-Time Dynamic Behaviour of the Ising-Like Phase Transition in Square-Lattice Fully Frustrated XY Models

Meng‐Bo Luo, Qing‐Hu Chen, Zhengkuan Jiao

Published Jul 30, 2002• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/19/8/338

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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.
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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.
The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated XY\mathrm{XY}XY model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings is investigated using Monte Carlo simulations. When x<1/2x<1/\sqrt{2}x<1/2​ (x(x(x is the ratio between NNN and NN couplings), the transition temperature Tc{T}_{c}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 1/2,1/\sqrt{2},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\mathrm{FF}\mathrm{XY}FFXY model, with or without NNN coupling, are in the same universality class. When x>1/2,x>1/\sqrt{2},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)].
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.