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In this paper we present numerical analysis of the phase transition of thearea-interaction model, which is a standard model of Statistical Mechanics. Thetheoretical results are based on a recent paper by Dereudre \& Houdebert\cite{dereudre_houdebert_2018_SharpTransitionWR} which provides a completephase diagram except on a bounded (implicit) domain. With our numericalanalysis we give an approximative explicit description of this domain. %Thisregion is related to the theoretical function $\beta \mapsto\widetilde{z}_c^a(\beta, 1)$ which is percolation threshold of the model, forgiven $\beta$. %We provide a numerical approximation of this function in orderto fully understand the phase diagram. Furthermore our numerical resultsconfirm the still unproven conjecture stating that non-uniqueness holds if andonly if $z= \beta$ is large enough, with a value of the threshold obtained fromthe simulation of $\beta_c \simeq 1.726$.

Numerical study for the phase transition of the area-interaction model