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

Abstract

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. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$. The structural properties of the network are investigated which show that that the small world behaviour is obtained along the line $\alpha =\frac{\ln (N/2p)}{\ln N}$, 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 Ising model evolves and their boundaries.

5 pages, 9 figures

References in corpus (3)

• Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions