论文标题
区域相互作用模型相变的数值研究
Numerical study for the phase transition of the area-interaction model
论文作者
论文摘要
在本文中，我们介绍了面积相互作用模型的相变的数值分析，该模型是统计力学的标准模型。理论结果基于Dereudre \＆houdebert \ cite {dereudre_houdebert_2018_sharptransitionwr}的最新论文，该论文提供了一个完整的相图，除了（隐式）域（隐式）域。通过我们的数值分析，我们对该域进行了近似的明确描述。 ％该区域与理论函数$β\ mapsto \ widetilde {z} _c^a（β，1）$，这是模型的渗透阈值，对于给定的$β$。 ％我们提供此功能的数值近似值，以便充分了解相图。此外，我们的数值结果证实了仍然未经证实的猜想，表明当且仅当$ z =β$足够大时，非唯一性才能达到，并且从$β_C\ simeq 1.726 $的仿真中获得的阈值值。
In this paper we present numerical analysis of the phase transition of the area-interaction model, which is a standard model of Statistical Mechanics. The theoretical results are based on a recent paper by Dereudre \& Houdebert \cite{dereudre_houdebert_2018_SharpTransitionWR} which provides a complete phase diagram except on a bounded (implicit) domain. With our numerical analysis we give an approximative explicit description of this domain. %This region is related to the theoretical function $β\mapsto \widetilde{z}_c^a(β, 1)$ which is percolation threshold of the model, for given $β$. %We provide a numerical approximation of this function in order to fully understand the phase diagram. Furthermore our numerical results confirm the still unproven conjecture stating that non-uniqueness holds if and only if $z= β$ is large enough, with a value of the threshold obtained from the simulation of $β_c \simeq 1.726$.
