Phase transitions in Ising model on a Euclidean network

Abstract

A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l)\propto l^{-\delta }$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbours apart from their nearest neighbours for $0\le \delta <2$. It is observed that there is a finite temperature phase transition in the entire range. For $0\le \delta <1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\le \delta \le 2$, the exponents depend on $\delta$. The results are discussed in the context of earlier observations on the topology of the underlying network.

7 pages, revtex4, 7 figures; to appear in Physical Review E, minor changes made

References in corpus (3)

• The spatial structure of networks
• Exact Solution of Ising Model on a Small-World Network
• Is small-world network disordered?

Cited by in corpus (4)

• Critical phenomena in complex networks
• Promote cooperation by localised small-world communication
• Phase transition of a one-dimensional Ising model with distance-dependent connections
• Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links