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Phase transition of a one-dimensional Ising model with distance-dependent connections

YunFeng Chang·Liang Sun·Xu Cai
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Abstract

The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $Θ(l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising model on networks with different $m$ values, this paper discusses the impact of the global correlation, which decays with the increase of $m$, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter $[< M>]$, it is observed that in the whole range of $0<m<2$, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.

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YunFeng Chang, Liang Sun, Xu Cai. 2007-05-22. Phase transition of a one-dimensional Ising model with distance-dependent connections. https://doi.org/10.1103/physreve.76.021101

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