Clusterization, frustration and collectivity in random networks

We consider the random Erdős–Rényi network with enhanced clusterization and Ising spins s = ±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 Tc 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 TSG; this temperature decreases with C, on the contrary to the mean field calculations. The results are interpreted in terms of social systems. PACS numbers: 89.65.-s, 64.90.+b