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arXiv:cond-mat/9705222 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Universal short-time behavior of the dynamic fully frustrated XY model

H. J. Luo, Lothar Schülke, Bo Zheng

Published Feb 1, 1998• 29 citations
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Abstract

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.

DOI
10.1103/physreve.57.1327

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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 \ensuremathθ\ensuremath{\theta}\ensuremathθ is measured for different temperatures and with different algorithms.
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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, $2\ensuremath{\beta}/\ensuremath{\nu},$ 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)].