Active-absorbing phase transition and small-world behaviour in Ising model on finite addition type networks in two dimensions

摘要

We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly from a total of N lattice sites. The total number of shortcuts added is controlled by two parameters p and alpha for fixed N. The structural properties of the network are investigated which show that the small-world behaviour is obtained along the line alpha = ln(N/2p)/ln N, which separates regions with ultra-small world like behaviour and short-ranged lattice like behaviour. We obtain a rich phase diagram in the p - alpha plane showing the existence of different types of active and absorbing states to which the Ising model evolves to and their boundaries.