论文标题
分析Glauber动力学下的远程ISING模型的有限尺寸效应
Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics
论文作者
论文摘要
我们考虑了Glauber动力学下的远程ISING模型，并使用扰动理论计算了有限大小系统中平均场近似值的差异。为了处理BBGKY层次结构，我们假设某些类型的广泛特性具有高斯分布，事实证明，这与柯克伍德叠加近似值等同于一阶扰动范围内。经过几次计算，得出了描述两体相关时间发展的普通微分方程。讨论是我们先前的研究的概括，该研究对无限范围的Ising模型产生了类似的考虑。计算结果符合数值模拟的结果，即相互作用的衰减足够缓慢。但是，当衰变变得迅速时，它们表现出不同的行为。
We considered a long-range Ising model under Glauber dynamics and calculated the difference from the mean-field approximation in a finite-size system using perturbation theory. To deal with the BBGKY hierarchy, we assumed that certain types of extensive properties have a Gaussian distribution, which turned out to be equivalent to the Kirkwood superposition approximation within the range of first-order perturbation. After several calculations, ordinary differential equations that describe the time development of a two-body correlation were derived. This discussion is the generalization of our previous study which developed a similar consideration on the infinite-range Ising model. The results of the calculation fit those of the numerical simulations for the case in which the decay of the interaction was sufficiently slow; however, they exhibited different behaviors when the decay became rapid.
