Restoring site percolation on a damaged square lattice

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dc.creatorGalam, Serge
dc.creatorMalarz, Krzysztof
dc.date2004-08-16
dc.date.accessioned2026-07-07T02:59:47Z
dc.date.available2026-07-07T02:59:47Z
dc.descriptionWe study how to restore site percolation on a damaged square lattice with nearest neighbor (N$^2$) interactions. Two strategies are suggested for a density $x$ of destroyed sites by a random attack at $p_c$. In the first one, a density $y$ of new sites are created with longer range interactions, either next nearest neighbor (N$^3$) or next next nearest neighbor (N$^4$). In the second one, new longer range interactions N$^3$ or N$^4$ are created for a fraction $v$ of the remaining $(p_c-x)$ sites in addition to their N$^2$ interactions. In both cases, the values of $y$ and $v$ are tuned in order to restore site percolation which then occurs at new percolation thresholds, respectively $π_3$, $π_4$, $π_{23}$ and $π_{24}$. Using Monte Carlo simulations the values of the pairs $\{y, π_3 \}$, $\{y, π_4\}$ and $\{v, π_{23}\}$, $\{v, π_{24}\}$ are calculated for the whole range $0\leq x \leq p_c(\text{N}^2)$. Our schemes are applicable to all regular lattices.
dc.description5 pages, revtex4
dc.identifierhttps://arxiv.org/abs/cond-mat/0408359
dc.identifierhttp://arxiv.org/abs/cond-mat/0408359
dc.identifierPhys. Rev. E72 (2005) 027103
dc.identifierdoi:10.1103/PhysRevE.72.027103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/24649
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleRestoring site percolation on a damaged square lattice
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