Affiliation:
1. Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India
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.
Funder
Department of Science and Technology-INSPIRE Fellowship
Science and Engineering Research Board
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization,Management Science and Operations Research,Computer Networks and Communications
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