Nam Keekwon, Kim Bongsoo, Lee Sung Jong
Department of Physics, Changwon National University, Changwon 641-773, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056104. doi: 10.1103/PhysRevE.77.056104. Epub 2008 May 13.
The static and dynamic critical properties of the ferromagnetic q -state Potts models on a square lattice with q=2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are investigated, from which static and dynamic critical exponents can be obtained. We find that the static exponents thus obtained from the relaxation of the order parameter and energy together with the second moments of the order parameter exhibit a close agreement with the exact exponents, especially for the case of the q=2 (Ising) model, when care is taken in the choice of the initial states for the relaxation of the second moments. As for the case of q=3 , the estimates for the static exponents become less accurate, but still exhibit reasonable agreement with the exactly known static exponents. The dynamic critical exponent for the q=2 (Ising) model is estimated from the relaxation of the second moments of the order parameter with mixed initial conditions to give z(q=2) approximately 2.1668(19) .
通过非平衡弛豫方法对q = 2和3的正方晶格上的铁磁q态Potts模型的静态和动态临界性质进行了数值研究。研究了序参量、能量以及二阶矩的弛豫行为，从中可以得到静态和动态临界指数。我们发现，从序参量和能量的弛豫以及序参量的二阶矩得到的静态指数与精确指数表现出密切的一致性，特别是对于q = 2（伊辛）模型，当在选择用于二阶矩弛豫的初始态时加以注意的情况下。对于q = 3的情况，静态指数的估计变得不太准确，但仍与已知的精确静态指数表现出合理的一致性。通过具有混合初始条件的序参量二阶矩的弛豫来估计q = 2（伊辛）模型的动态临界指数，得到z(q = 2)约为2.1668(19) 。
