随机网络中三种渗流相变的交叉

Crossover of three percolation transitions types in random networks

摘要:

基于一个简单的分段线性权函数, 研究了参数α统一两种不同三临界的渗流模型，当调节α的值从1到0渗流相变从连续变化到多重不连续和不连续.通过计算不同系统尺寸下序参量的相对方差，表明α=0.6时在热力学极限下跌落为一个奇异峰，α=0.5时在某个超临界区交织在一起，α=0.4时在一个延伸的区间上随系统尺寸的增加变得更大.因此对于相变从连续变化到多重不连续和从多重不连续变化到不连续，三相点分别位于0.6和0.5以及0.4和0之间.该框架为理解随机网络中不同类型相变之间的交叉行为提供了见解.

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.