Topological effects and conformal invariance in long-range correlated random surfaces

arXiv: Statistical Mechanics Pub Date : 2020-05-24 DOI:10.21468/SCIPOSTPHYS.9.4.050

Nina Javerzat, S. Grijalva, A. Rosso, R. Santachiara

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引用次数: 6

Abstract

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq-\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-\frac{3}{4}

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长程相关随机曲面的拓扑效应和共形不变性

我们考虑具有负Hurst指数的离散随机分形曲面$H<0$。通过激活表面高度大于给定水平$h$的位置，可以提供晶格的随机着色。激活位点的集合通常表示为偏移集。该集合的连接组件，即水平簇，定义了在站点占用中具有长期相关性的单参数($H$)渗透模型族。水平簇渗透在一个有限值$h=h_c$，对于$H\leq-\frac{3}{4}$，相变预计将保持在纯(即不相关)渗透的相同普适类中。相反，对于$-\frac{3}{4}

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arXiv: Statistical Mechanics

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