ontinuous percolation phase transitions of random networks under a generalized Achlioptas process

Using finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdos-Renyi network at p = 0.5 and the random network under the Achlioptas process at p = 1. Using both the fixed point of the size ratio s(2)/s(1) and the straight line of ln s(1), where s(1) and s(2) are the reduced sizes of the largest and the second-largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 <= p <= 1. From the slopes of ln s(1) and ln(s(2)/s(1))' at the critical point, we get critical exponents beta and upsilon of the phase transitions. At 0.5 <= p = 0.9, beta, upsilon, and s(2)/s(1) at critical point vary with p and the universality class of phase transitions depends on p.