2020/03/24 by Pierre Houdebert, Houdebert, Pierre
Materials Science · Mathematics · Physics and Astronomy · #82B21 60E15 60K35 60G55 82B43 60D05 #FOS: Mathematics #Material Dynamics and Properties #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2003.10754
openalex publication_date 2020/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citedereudrehoudebert2018SharpTransitionWR 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↦ \widetildezca(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 βc ≃ 1.726.