arXiv:cond-mat/9801253 · Physical Review Letters

Dynamic Approach to the Fully Frustrated XY Model

H. J. Luo, Lothar Schülke, Bo Zheng

Published Jul 6, 1998• 113 citations

Abstract

Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated $\mathrm{XY}$ model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature ${T}_{c}$ and all the dynamic and static critical exponents $\ensuremath{\theta}$, $z$, $\ensuremath{\beta}$, and $\ensuremath{\nu}$.

DOI: 10.1103/physrevlett.81.180

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arXiv:cond-mat/9801253 · Physical Review Letters

Dynamic Approach to the Fully Frustrated XY Model

H. J. Luo, Lothar Schülke, Bo Zheng

Published Jul 6, 1998• 113 citations

arXiv HTML PDF

Abstract

Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated

\mathrm{XY}

model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature

{T}_{c}

and all the dynamic and static critical exponents

\ensuremath{\theta}

z

\ensuremath{\beta}

, and

\ensuremath{\nu}

DOI: 10.1103/physrevlett.81.180

Related papers

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

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

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)].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)].

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Ising-like phase transition in the fully frustrated XY model with weak disorder

Huijun Liu, Jian-Ping Lv, Q.-H. Chen

Europhysics Letters (EPL)Dec 1, 20082 citations

Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated

\mathrm{XY}

model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature

{T}_{c}

and all the dynamic and static critical exponents

\ensuremath{\theta}

z

\ensuremath{\beta}

, and

\ensuremath{\nu}

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)].

{\mathit{T}}_{\mathit{U}(1)}

=0.446, which is about 7% above the estimated chiral critical temperature

{\mathit{T}}_{\mathit{Z}2}

=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.

With Monte Carlo methods we investigate the dynamic relaxation of the fully frustrated

\mathrm{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.