Active-absorbing phase transition and small-world behaviour in Ising model on finite addition type networks in two dimensions. (27th January 2020)

• Record Type: Journal Article
• Authors: Mullick, Pratik; Sen, Parongama
• Editors: Gomez-Gardenes, Jesus
• Is Part Of: Journal of complex networks. Volume 8:Number 1(2020)
• Publication Date: 2020-01-27
• Subjects: active-absorbing phase transition -- phase diagram -- small-world network -- average shortest distance -- clustering -- Monte Carlo simulation; Numerical analysis -- Periodicals; Computer networks -- Periodicals; Social networks -- Periodicals; 518.05
• DOI: 10.1093/comnet/cnz046
• Languages: English
• ISSNs: 2051-1310

Abstract

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 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 $\alpha=\frac{\ln (N/2p)}{\ln N}$, 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 the Ising model evolves to and their boundaries.