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One-dimensional Ising model built on small-world networks: competing dynamics

Wei Liu·Wen-Yuan Xiong·Jian-Yang Zhu
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Abstract

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect.

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Wei Liu, Wen-Yuan Xiong, Jian-Yang Zhu. 2005-05-13. One-dimensional Ising model built on small-world networks: competing dynamics. https://doi.org/10.1103/physreve.71.056123

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