Universality class of explosive percolation in Barabási-Albert networks

Abstract

In this work, we study explosive percolation (EP) in Barabási-Albert (BA) network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For m = 1 we find that the critical point tc = 1 which is the maximum possible value of the relative link density t; Hence we cannot have access to the other phase like percolation in one dimension. However, for m > 1 we find that tc decreases with increasing m and the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR. It implies that they all belong to the same universality class like EP in the Erdös-Rényi network. Besides, the critical exponents obey the Rushbrooke inequality α + 2β + γ ≥ 2 but always close to equality. PACS numbers: 61.43.Hv, 64.60.Ht, 68.03.Fg, 82.70.Dd.