标题： 自旋模型和SU(N)规范理论中的聚类渗透与临界行为 显示英文标题

标题： Cluster Percolation and Critical Behaviour in Spin Models and SU(N) Gauge Theories

摘要： 几个自旋模型的临界行为可以简单地描述为某种适当定义的团簇或液滴的渗流：几何相变的开始与临界点重合，且渗流指数等于热力学指数。 目前尚不清楚，对于一个给定的模型，是否能够定义出液滴。 在有可能的情况下，液滴的定义一般依赖于具体研究的模型，并可能相当复杂。 我们在这里提出一个简单的通用定义：液滴是通过将同号最近邻自旋以一定的键概率 \(p_B\) 连接起来形成的团簇，\(p_B\) 是允许在临界温度 \(T_c\) 下存在渗透团簇的最小概率。 通过晶格蒙特卡洛模拟，我们发现这个定义确实满足了对于许多经典自旋模型（离散和连续）在二维和三维情况下液滴所需满足的条件。 特别是，我们的方法允许精确描述 SU(N) 规范理论中的禁闭-去禁闭相变作为波利亚科夫环的渗透。 显示英文摘要

摘要： The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are equal to the thermal exponents. It is still unknown whether, given a model, one can define at all the droplets. In the cases where this is possible, the droplet definition depends in general on the specific model at study and can be quite involved. We propose here a simple general definition for the droplets: they are clusters obtained by joining nearest-neighbour spins of the same sign with some bond probability p_B, which is the minimal probability that still allows the existence of a percolating cluster at the critical temperature T_c. By means of lattice Monte Carlo simulations we find that this definition indeed satisfies the conditions required for the droplets, for many classical spin models, discrete and continuous, both in two and in three dimensions. In particular, our prescription allows to describe exactly the confinement-deconfinement transition of SU(N) gauge theories as Polyakov loop percolation.