Percolation-like phase transition in a non-equilibrium steady state

Bose, Indrani ; Chaudhuri, Indranath (2001) Percolation-like phase transition in a non-equilibrium steady state International Journal of Modern Physics C, 12 . 247_1-247_23. ISSN 0129-1831

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We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let p be the site occupation probability of the square lattice. For p greater than a critical value pc, the steady state consists of stripe-like patterns with long-range connectivity. For p < pc, the connectivity is lost. The value of pc is found to be much greater than that of the site percolation threshold for the square lattice. In the vicinity of pc, the cluster-related quantities exhibit power-law scaling behaviour. The method of finite-size scaling is used to determine the values of the fractal dimension df , the ratio, γ/ν, of the average cluster size exponent γ and the correlation length exponent ν and also ν itself. The values appear to indicate that the disordered GM model belongs to the universality class of ordinary percolation.

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Source:Copyright of this article belongs to World Scientific Publishing Company.
ID Code:93734
Deposited On:25 Jun 2012 13:10
Last Modified:19 May 2016 06:45

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