Constrained volume-difference site percolation model on the square lattice

Charles S. do Amaral

Physica A: Statistical Mechanics and its Applications, 2025, vol. 663, issue C

Abstract: We study a percolation model with restrictions on the opening of sites on the square lattice. In this model, each site s∈Z2 starts closed and an attempt to open it occurs at time t=ts, where (ts)s∈Z2 is a sequence of independent random variables uniformly distributed on the interval [0,1]. The site will open if the volume difference between the two largest clusters adjacent to it is greater than or equal to a constant r or if it has at most one adjacent cluster. Through numerical analysis, we determine the critical threshold tc(r) for various values of r, verifying that tc(r) is non-decreasing in r and that there exists a critical value rc=5 beyond which percolation does not occur. Additionally, we find that the correlation length exponent of this model is equal to that of the ordinary percolation model. For t=1 and 1≤r≤9, we estimate the averages of the density of open sites, the number of distinct cluster volumes, and the volume of the largest cluster.

Keywords: Percolation; Constrained percolation; Complex networks; Lattice models (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:663:y:2025:i:c:s0378437125000834

DOI: 10.1016/j.physa.2025.130431

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