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Physical review. B, Condensed matter

Second-order phase transition in the fully frustrated XY model with next-nearest-neighbor coupling

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

Published Nov 8, 2001• 15 citations
Publisher

Abstract

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

DOI
10.1103/physrevb.64.212403

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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\ensuremathβ/\ensuremathν,2\ensuremath{\beta}/\ensuremath{\nu},2\ensuremathβ/\ensuremathν, and \ensuremathν\ensuremath{\nu}\ensuremathν 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\ensuremathβ/\ensuremathν2\ensuremath{\beta}/\ensuremath{\nu}2\ensuremathβ/\ensuremathν and \ensuremathν\ensuremath{\nu}\ensuremathν 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)].
Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY\mathrm{XY}XY model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature Tc{T}_{c}Tc​ and all the dynamic and static critical exponents $\ensuremath{\theta}$, zzz, $\ensuremath{\beta}$, and $\ensuremath{\nu}$.
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.
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.
In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.
With Monte Carlo methods we investigate the dynamic relaxation of the fully frustrated XY\mathrm{XY}XY model in two dimensions below and at the Kosterlitz-Thouless phase transition temperature. Special attention is given to the sublattice structure of the dynamic evolution. The short-time scaling behavior is found and universality confirmed. The critical exponent $\ensuremath{\theta}$ is measured for different temperatures and with different algorithms.