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

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