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arXiv · 1908.10656

Active-absorbing phase transition and small world behaviour in Ising model on finite addition type networks in two dimensions

Pratik Mullick·Parongama Sen
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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. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$. The structural properties of the network are investigated which show that 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 Ising model evolves and their boundaries.

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Pratik Mullick, Parongama Sen. 2019-08-28. Active-absorbing phase transition and small world behaviour in Ising model on finite addition type networks in two dimensions. https://doi.org/10.1093/comnet%2Fcnz046

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