三维X-Y模型的滞后标度和动态相变行为

Hysteretic scaling and dynamical phase transition of three-dimension X-Y Model

采用MonteCarlo方法对 3DX Y模型进行数值模拟计算 ,研究了在非线性外场驱动下 3DX Y模型的滞后标度和动态相变 .得出了滞后标度关系为Area～hα0 ωβ( 1-T Tc) γ,其中α =0 5 7,β =0 34,γ =0 90 .发现其动态相变行为在一定的临界参数条件下 ,初始短周期 (周期数PN≤ 10 )内的结果具有与Ising模型类似的对称性破缺 ;但在长周期内 (PN≥ 2 0 0 )的结果则明显区别于Ising模型而与Heisenberg模型相近 。

We have studied in this paper,by performing the Monte Carlo numerical simulation,both the hysteretic scaling and the dynamical phase transition of a three-dimensional, (3D) classical X-Y model driven by an sinusoidally oscillating external magnetic field. A scaling formula has been worked out which relates the hysteresis loop area with the amplitude h(0) and frequency omega of the external field as well as the reduced temperature T/T-c. of the system in the form: Area similar to h(0)(alpha)omega(beta) (1 - T/T-c)(gamma). The best-fit exponents are alpha = 0.57, beta = 0.34 and gamma = 0.9. The 3D X-Y model also characterizes a distinctive discrepancy in dynamical transition feature after short and long term evolution of magnetization, respectively. Our simulation disclosed that the short-term evolution of magnetization (period number less than or equal to 10) attains the symmetry-breaking of system with a nonzero dynamical order parameter (Q not equal 0) at a either critical amplitude h(0c) or frequency omega(c). The symmetry-breaking in short term, however, evolves steadily into a symmetric disorder state (Q = 0) after a longer term relaxation of system. The specific relaxation times at which the Q value becomes zero from nonzero increase evidently as the temperature of system drops.