The Study On Phase Transition Of Explosive Percolation Under The Rules Of Local Choice

Percolation model is an important geometric phase transition for the study of phase transitions and critical phenomena. Percolation model can lead to the phase transition of macro structural properties in the system, only by setting some simple rules on occupying sites and bonds. It has a wide range of researches and applications in thermodynamics and statistical physics, and many engineering fields. Explosive percolation is a very interesting scientific problem, because a slight modification of the classical selection rules can significantly alter the critical behavior of the percolation phase transition.Different from the global random selection rules, a local rule is proposed in this thesis, which limits the selection process in a window. Based on the rule, explosive percolation model on two kinds of regular lattices is studied by Monte Carlo simulations. Through the analysis of measurement, it’s proved that this local rule can generate explosive percolation and its critical behavior has a close relationship with the window size. A simulation study on different window size reveals the window size ratio which causes the most explosive phase transition. Meanwhile, the properties about explosion and continuity of phase transition under this local rule are compared with those in classical percolation and best-of-m model.The first two parts introduce the fundamental principles, the research background and some common numerical simulation methods of explosive percolation. The research findings and shortcomings of the percolation under the local selection rule are analyzed and discussed in detail in last two parts.