Q factor: A measure of competition between the topper and the average in percolation and in self-organized criticality

Article Type

Research Article

Publication Title

Physical Review E

Abstract

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 Qmax(L) at a specific value pmax(L) and then gradually decays. Our numerical study of site percolation problems on the square, triangular, and simple cubic lattices exhibits that the asymptotic values of pmax, though close, are distinct from the corresponding percolation thresholds of these lattices. We also show, using scaling analysis, that at pmax the value of Qmax(L) diverges as Ld (d denoting the dimension of the lattice) as the system size approaches its asymptotic limit. We further extend this idea to nonequilibrium systems such as the sandpile model of self-organized criticality. Here the Q(ρ,L) factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches, with ρ the drop density of the driving mechanism. This study was prompted by some observations in sociophysics.

DOI

10.1103/PhysRevE.110.014131

Publication Date

7-1-2024

Comments

Open Access; Green Open Access

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