Finite-size effects in exponential random graphs and cluster evaporation

Abstract

In this Letter we find numerically the strong finite-size effects in the critical behavior of Erdős-Rényi (ER) networks supplemented with chemical potentials for some motifs, in particular 2-stars and triangles. For the 2-star model above the critical value of the chemical potential a ground state looks as star-like graph with the finite set of hubs at ER parameter $p<0.5$ or as the single cluster at $p>0.5$. It is found that there exists the critical value of number of nodes $N^{\ast }(p)$ when the ground state undergoes clear-cut crossover and at $N>N^{\ast }(p)$ the network flows via a cluster evaporation to the state involving the small star in the ER environment. The similar evaporation of the cluster takes place at $N>N^{\ast }(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime. The possible analogies concerning the strong entropic finite-size effects in the holographic description of matrix black hole (BH) formation and evaporation are mentioned.

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Cited by in corpus (1)

• Phase transitions in atypical systems induced by a condensation transition on graphs