PHASE TRANSITION IN THE ISING MODEL ON LOCAL-WORLD EVOLVING NETWORKS

摘要

We study the critical behavior of the Ising model on the local-world evolving network. Monte Carlo simulations with the standard Metropolis local update algorithms are performed extensively on the network with different parameters. Ising spins put onto network vertices exhibit an effective phase transition from ferromagnetism to paramagnetism upon heating. The critical temperature has been demonstrated to increase linearly with the average degree of the network as T-C similar to < k >. Simulation results on local-world evolving networks with various parameters show logarithmical relationships of the critical temperature with the size of the local world as T-C similar to ln(m(l)), and with the size of the network as T-C similar to ln(N), respectively. The latter is the generalization of the conclusion for the Ising model on the Barabasi-Albert scale-free network, a limiting case of the local-world evolving network.