Clusterization, frustration and collectivity in random networks

Abstract

We consider the random Erd{\H o}s--R\'enyi network with enhanced clusterization and Ising spins $s=\pm 1$ at the network nodes. Mutually linked spins interact with energy $J$. Magnetic properties of the system as dependent on the clustering coefficient $C$ are investigated with the Monte Carlo heat bath algorithm. For $J>0$ the Curie temperature $T_c$ increases from 3.9 to 5.5 when $C$ increases from almost zero to 0.18. These results deviate only slightly from the mean field theory. For $J<0$ the spin-glass phase appears below $T_{SG}$; this temperature decreases with $C$, on the contrary to the mean field calculations. The results are interpreted in terms of social systems.