Phase transitions in Ising model on a Euclidean network

Arnab Chatterjee; Parongama Sen

doi:10.1103/physreve.74.036109

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arXiv · cond-mat/0606138

Phase transitions in Ising model on a Euclidean network

Arnab Chatterjee·Parongama Sen

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Abstract

A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-δ}$ 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 $0 \leq δ< 2$. It is observed that there is a finite temperature phase transition in the entire range. For $0 \leq δ< 1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\leq δ\leq 2$, the exponents depend on $δ$. The results are discussed in the context of earlier observations on the topology of the underlying network.

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BibTeX RIS

Arnab Chatterjee, Parongama Sen. 2006-08-02. Phase transitions in Ising model on a Euclidean network. https://doi.org/10.1103/physreve.74.036109

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