Huang Xianzhi, Gong Shurong, Zhong Fan, Fan Shuangli
State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Zhongshan University, Guangzhou 510275, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 1):041139. doi: 10.1103/PhysRevE.81.041139. Epub 2010 Apr 30.
We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.
我们将有限时间标度应用于二维晶格上q = 3和4的q态Potts模型，以确定其临界性质。这包括对模型施加一个线性变化的外场，该外场与q个状态之一耦合，以在临界附近操纵其动力学，并使系统偏离平衡，从而产生滞后现象，以及定义一个不同于通常的序参量和一个非平衡磁化率，以提取矫顽场。从序参量、矫顽力、滞后面积及其导数的有限时间标度中，我们能够系统地确定静态和动态临界指数以及临界温度。一般得到的静态临界指数，特别是磁指数δ，与推测值相当吻合。得到的动态临界指数似乎证实了所提出的动态弱普适性，但不太可能与q = 4的最近短时间动态结果一致。我们的结果还提出了一种表征弱普适性的替代方法。
