Park Jinha, Yi Sudo, Kahng B
CCSS, CTP, and Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea.
School of Physics, Korea Institute for Advanced Study, Seoul 02455, South Korea.
Chaos. 2020 May;30(5):051102. doi: 10.1063/5.0008189.
Phase transitions (PTs) are generally classified into second-order and first-order transitions, each exhibiting different intrinsic properties. For instance, a first-order transition exhibits latent heat and hysteresis when a control parameter is increased and then decreased across a transition point, whereas a second-order transition does not. Recently, hybrid percolation transitions (HPTs) are issued in diverse complex systems, in which the features of first-order and second-order PTs occur at the same transition point. Thus, the question whether hysteresis appears in an HPT arises. Herein, we investigate this fundamental question with a so-called restricted Erdős-Rényi random network model, in which a cluster fragmentation process is additionally proposed. A hysteresis curve of the order parameter was obtained. Depending on when the reverse process is initiated, the shapes of hysteresis curves change, and the critical behavior of the HPT is conserved throughout the forward and reverse processes.
相变（PTs）通常分为二级相变和一级相变，每一种都表现出不同的内在特性。例如，当控制参数在一个转变点处先增加然后减小时，一级相变表现出潜热和滞后现象，而二级相变则不会。最近，在各种复杂系统中出现了混合渗流转变（HPTs），其中一级和二级PTs的特征出现在同一个转变点。因此，HPT中是否会出现滞后现象这一问题就产生了。在此，我们用一个所谓的受限厄尔多斯 - 雷尼随机网络模型来研究这个基本问题，在该模型中还额外提出了一个簇碎裂过程。得到了序参量的滞后曲线。根据反向过程启动的时间不同，滞后曲线的形状会发生变化，并且HPT的临界行为在正向和反向过程中都是守恒的。
