Ising模型实空间重正化的Monte Carlo模拟

Monte Carlo Simulation of Real Space Renormalization

以二维正方晶格Ising模型为例,采用Monte Carlo方法模拟实空间重正化群操作,分别采用简单抽样和重要性抽样。对于简单抽样,可以得到解析解,但模拟的元胞不大;而对于重要性抽样,虽然只能获得数值解,但是可以模拟很大的元胞,结果也更接近精确解;文中的方法使实空间重正化群操作的精度大大提高。

Mont Carlo simulation of the renormalization, using simple sampling and important sampling, respectively. For simple sampling, analytical result is got, but only small cell can be simulated; Comparatively, the much larger cell can be simulated using. And the obtained numerical solution becomes closer to the accurate result. The method of this article can highly improve the accuracy of real space renormalization.