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arXiv:cond-mat/9807142 · Modern Physics Letters B

Dynamic Monte Carlo Study of the Two-Dimensional Quantum XY Model

H.-P. Ying, H. J. Luo, Lothar Schülke, Bo Zheng

Published Dec 30, 1998• 18 citations
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Abstract

We present a dynamic Monte Carlo study of the spin-1/2 quantum XY model in two-dimensions at the Kosterlitz–Thouless phase transition temperature. The short-time dynamic scaling behaviour is found and the dynamical exponents θ, z and the static exponent η are determined.
DOI
10.1142/s0217984998001463

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Based on the short-time dynamic scaling form, a dynamic approach is proposed to numerically tackle the Kosterlitz-Thouless phase transition. Taking the two-dimensional XY\mathrm{XY}XY model as an example, the exponential divergence of the spatial correlation length, the transition temperature TKT,{T}_{\mathrm{KT}},TKT​, and all critical exponents are computed. Compared with Monte Carlo simulations in equilibrium, we obtain data at temperatures closer to TKT.{T}_{\mathrm{KT}}.TKT​.
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.