一种模拟宏观系统临界点的有效算法
An efficient algorithm simulating a macroscopic system at the critical point
摘要：
众所周知，由于相应的弛豫时间（临界慢化）的发散，传统的模拟算法对于精确地在临界点处的宏观系统的统计描述是低效的。另一方面，在序参量空间中的动力学在这种情况下由于相关波动模式中的自相似性的发生而显著简化。因此，临界点处的有效作用获得了非常简单的形式。在目前的工作中，我们表明，这种简化的行动，可以用来有效地模拟宏观系统的统计性质，正是在临界点。使用所提出的算法，我们生成一个合奏的配置类似的特征分形几何的临界系统相关的自相似序参量波动。作为一个例子，我们模拟的一个组件的实标量场理论在过渡点$T=T_c$作为一个代表系统属于$3-D$伊辛普适类。
英文摘要：
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing down). On the other hand the dynamics in the order parameter space is simplified significantly in this case due to the onset of self-similarity in the associated fluctuation patterns. As a consequence the effective action at the critical point obtains a very simple form. In the present work we show that this simplified action can be used in order to simulate efficiently the statistical properties of a macroscopic system exactly at the critical point. Using the proposed algorithm we generate an ensemble of configurations resembling the characteristic fractal geometry of the critical system related to the self-similar order parameter fluctuations. As an example we simulate the one-component real scalar field theory at the transition point $T=T_c$ as a representative system belonging to the $3-D$ Ising universality class.
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