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Site percolation thresholds in discrete systems with inhomogeneous occupation

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  • Lebrecht, W.

Abstract

Discrete systems with spatially inhomogeneous occupation are analyzed using triangular and square elementary cells, in which the occupation probability depends on the position of the central site. As a first approximation, a first order parameterization is introduced for both geometries, assigning different probabilities to the central site and its nearest neighbors. Subsequently, in the case of the square lattice, the formulation is extended to the second order by incorporating the contribution of the corner sites, allowing for a more detailed description of the spatial structure of connectivity. Based on an exact classification of percolating configurations, a master equation is constructed for each geometry, whose derivative enables the determination of the percolation threshold via the Rosowsky method, correctly recovering the homogeneous case as a particular limit.

Suggested Citation

  • Lebrecht, W., 2026. "Site percolation thresholds in discrete systems with inhomogeneous occupation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 697(C).
    • Handle: RePEc:eee:phsmap:v:697:y:2026:i:c:s0378437126004322
    DOI: 10.1016/j.physa.2026.131696
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