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arxiv: cond-mat/0306017 · v1 · submitted 2003-06-02 · ❄️ cond-mat.stat-mech

Phase transition in the Ising model on a small-world network with distance-dependent interactions

classification ❄️ cond-mat.stat-mech
keywords alphainteractionsystemphasetransitionisinglong-rangenetwork
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We study the collective behavior of an Ising system on a small-world network with the interaction $J(r) \propto r^{-\alpha}$, where $r$ represents the Euclidean distance between two nodes. In the case of $\alpha = 0$ corresponding to the uniform interaction, the system is known to possess a phase transition of the mean-field nature, while the system with the short-range interaction $(\alpha\to\infty)$ does not exhibit long-range order at any finite temperature. Monte Carlo simulations are performed at various values of $\alpha$, and the critical value $\alpha_c$ beyond which the long-range order does not emerge is estimated to be zero. Thus concluded is the absence of a phase transition in the system with the algebraically decaying interaction $r^{-\alpha}$ for any nonzero positive value of $\alpha$.

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