论文标题
超级放慢键入的ISING模型
Super slowing down in the bond-diluted Ising model
论文作者
论文摘要
在统计物理学的模型中，动力学通常会在临界点附近大幅下降。通常，关键点的相关时间$τ$随着系统尺寸$ l $ in powerlaw时尚而增加：$τ\ sim l^z $，它定义了关键的动力学指数$ z $。我们表明，这也适用于制度$ P> p_c $中的2D债券删除的ISING模型，其中$ p $是表示债券浓度的参数，但具有动态的关键指数$ z（p）$，显示出强大的$ p $依赖性。此外，我们从数字上表明，从总磁化的自相关获得的$ z（p）$，当接近渗透阈值$ p_c = 1/2 $时出现不同：$ z（p）-z（1）\ sim（p_c）（p_c）^{ - 2} $。我们将观察到的相关时间与大小的相关时间非常快地增加为{\它超级放慢}。从临界点表现出异常扩散的总磁化均值偏差的独立测量数据支持了这一结果。
In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time $τ$ at the critical point increases with system size $L$ in power-law fashion: $τ\sim L^z$, which defines the critical dynamical exponent $z$. We show that this also holds for the 2D bond-diluted Ising model in the regime $p>p_c$, where $p$ is the parameter denoting the bond concentration, but with a dynamical critical exponent $z(p)$ which shows a strong $p$-dependence. Moreover, we show numerically that $z(p)$, as obtained from the autocorrelation of the total magnetisation, diverges when the percolation threshold $p_c=1/2$ is approached: $z(p)-z(1) \sim (p-p_c)^{-2}$. We refer to this observed extremely fast increase of the correlation time with size as {\it super slowing down}. Independent measurement data from the mean-square deviation of the total magnetisation, which exhibits anomalous diffusion at the critical point, supports this result.
