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首页> 外文期刊>Journal of Statistical Physics >Phase Diagram of Inhomogeneous Percolation with a Defect Plane
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Phase Diagram of Inhomogeneous Percolation with a Defect Plane

机译：具有缺陷平面的非均匀渗流的相图

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摘要

Let be the -dimensional hypercubic lattice and let be an -dimensional sublattice, with . We consider a model of inhomogeneous bond percolation on at densities and , in which edges in are open with probability , and edges in open with probability . We generalize several classical results of (homogeneous) bond percolation to this inhomogeneous model. The phase diagram of the model is presented, and it is shown that there is a subcritical regime for and (where is the critical probability for homogeneous percolation in ), a bulk supercritical regime for , and a surface supercritical regime for and . We show that is a strictly decreasing function for , with a jump discontinuity at . We extend the Aizenman-Barsky differential inequalities for homogeneous percolation to the inhomogeneous model and use them to prove that the susceptibility is finite inside the subcritical phase. We prove that the cluster size distribution decays exponentially in the subcritical phase, and sub-exponentially in the supercritical phases. For a model of lattice animals with a defect plane, the free energy is related to functions of the inhomogeneous percolation model, and we show how the percolation transition implies a non-analyticity in the free energy of the animal model. Finally, we present simulation estimates of the critical curve .
机译：设为三维超三次晶格，为带有的三维次晶格。我们考虑一个密度为的非均匀键渗模型，其中边的概率是开放的，边的概率是开放的。我们将（均质）键渗滤的几个经典结果推广到此不均质模型。给出了模型的相图，并表明存在和的亚临界状态（其中均匀渗透的临界概率），和的整体超临界状态和表面超临界状态。我们证明了是的一个严格递减函数，在处具有跳跃不连续性。我们将均匀渗流的Aizenman-Barsky微分不等式扩展到不均匀模型，并使用它们证明在亚临界相内磁化率是有限的。我们证明了簇大小分布在亚临界阶段呈指数衰减，而在超临界阶段呈指数衰减。对于具有缺陷平面的晶格动物模型，自由能与非均匀渗滤模型的功能相关，并且我们展示了渗滤过渡如何暗含动物模型的自由能的非解析性。最后，我们给出了临界曲线的仿真估计。

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