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Publication

Critical scaling for an anisotropic percolation system on Z(2)

Thomas Mountford, Hao Xue
2020
Journal Articles

Abstract

In this article, we consider an anisotropic finite-range bond percolation model on Z(2). On each horizontal layer {(x, i): x is an element of Z} we have edges for 1

Official source

https://infoscience.epfl.ch/entities/publication/f87c056b-30c8-4b8d-918b-e4c1a73505a4

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Thomas Mountford, Hao Xue
2020
Journal Articles

Abstract

In this article, we consider an anisotropic finite-range bond percolation model on Z(2). On each horizontal layer {(x, i): x is an element of Z} we have edges for 1

Official source

https://infoscience.epfl.ch/entities/publication/f87c056b-30c8-4b8d-918b-e4c1a73505a4

About this result

Related concepts (22)

Percolation theory

In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology).

Critical exponent

Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.

Percolation threshold

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them.

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Critical scaling for an anisotropic percolation system on Z(2)

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