Q-factor: A measure of competition between the topper and the average in percolation and in SOC
| Autor: | Ghosh, Asim, Manna, S. S., Chakrabarti, Bikas K. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 110, 014131 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.110.014131 |
| Popis: | We define the $Q$-factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability $p$ is increased, the $Q$-factor for the system size $L$ grows systematically to its maximum value $Q_{max}(L)$ at a specific value $p_{max}(L)$ and then gradually decays. Our numerical study of site percolation problems on the square, triangular and the simple cubic lattices exhibits that the asymptotic values of $p_{max}$ though close, are distinctly different from the corresponding percolation thresholds of these lattices. We have also shown using the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges as $L^d$ ($d$ denoting the dimension of the lattice) as the system size approaches to their asymptotic limit. We have further extended this idea to the non-equilibrium systems such as the sandpile model of self-organized criticality. Here, the $Q(\rho,L)$-factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches; $\rho$ being the drop density of the driving mechanism. This study has been prompted by some observations in Sociophysics. Comment: 9 pages, 13 figures |
| Databáze: | arXiv |
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