二维XY模型始于有序初态的aging现象

Aging Phenomenon of 2D XY Model Starting from an Ordered Intial State

应用蒙特卡罗数值模拟方法,对二维XY模型始于有序初态的aging现象展开研究。模拟温度设在临界温度附近,模拟的物理量为双时自关联函数A(t,t')。其难度在于对从有序初态开始的动力学过程,解析研究滞后于数值研究,因此对标度形式的推论成为热点。数值研究发现,非平衡态下的二维XY系统的自关联函数与空间关联长度之比ξ(t)/ξ(t')相关,在相变点附近具有标度行为,证实系统处于aging过程。更重要的是通过对双时自关联函数仔细的动力学标度分析,得到了与以往文献相比更为可信的标度形式。用数值方法证实了这种标度形式不仅在低温下成立,在临界温度附近也成立。因为与其他文献相比,本研究的模拟温度更接近临界点,并在这样的动力学标度下得到了正确的临界指数,说明本研究的实验数据是自洽和可信的,同时观察到不同等待时间下模拟实验数据的collapse现象。

With Monte Carlo simulation method,the aging phenomenon of the 2D XY model is numerically studied.Starting from an ordered initial state,the system is suddenly quenched to critical temperature Tc.The two-time autocorrelation function A（t,t＇） is measured.For a dynamic process with an ordered initial state,the difficult problem is that accurate analysis is lagging behind the Monte Carlo simulation study.So many activities have been devoted to dynamic scaling form.According to the numerical experimental data of 2D XY non-equilibrium system,the relation between A（t,t＇） and ratio of spatial correlation length is detected.The aging phenomenon exhibits a dynamic scaling behavior induced by the time correlation.The aging phenomenon is characterized by the dynamic scale invariance.The aging phenomenon of 2D XY model is confirmed.Especially,the correction of scaling behavior is numerically verified,the form of dynamic scaling of A（t,t＇） is more creditable than existing literatures.For a dynamic process starting from an ordered initial state,the scaling form assumption fits the numerical data well.The scaling form holds not only at lower temperatures but also around Tc.This is because of the simulation temperature is close to the critical temperature.Based on the dynamic scaling,the experimental data indicate that more accurate values of the critical exponents can be obtained.In addition,the data collapse phenomenon is observed.