2019/05/08 by Gorsky, A., Valba, O. · 1 citation
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1905.03336
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*(p) when the ground state undergoes clear-cut crossover and at N>N*(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*(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.