Crossover of three percolation transitions types in random networks

Abstract:

Based on a simple piecewise linear weighted function, we unified two different types of tricritical percolation with a parameter α in one model, in which by tuning α from 1 to 0 the phase transition can switch from continuous to multiple discontinuous to discontinuous. By calculating the relative variance of the order parameter with different system sizes, we find that it collapses to a singular peak at the critical point in the thermodynamical limit at α=0.6, and interlaces together on a supercritical interval at α=0.5, and becomes larger on an extended interval at α=0.4 with increasing system size, respectively. It shows that the tricritical value of α is between 0.6 and 0.5 as well as between 0.4 and 0 from continuous to multiple discontinuous as well as from multiple discontinuous to discontinuous respectively. Our framework provides insights into understanding the crossover behaviors between different types of phase transition in random networks.