Tuning the tricritical points of percolation transitions in random networks

Abstract

Percolation transition in networks as edges are gradually added, can generate a variety of critical and supercritical behaviors. Here we report a percolation transition model with two parameters α and β, in which by decreasing the value of α from 1 to 0 the phase transition could change from continuous to multiple discontinuous and finally to discontinuous without supercritical region, and that the corresponding tricritical points could be tuned by changing the value of β. In order to find out the tricritical point from continuous to multiple discontinuous, by investigating the cluster merging dynamics we find that it belongs to an interval and becomes larger with increasing value of β, and this result is verified by the distinctly different relative variance behaviors of the order parameter at the two endpoints of the interval. On the other hand, the tricritical point from multiple discontinuous to discontinuous is β/(1 + β), which also becomes larger when increasing the value of β. Our results might be helpful in controlling the width of phase transition region in random networks.