Nucleation of a three-state spin model on complex networks

Hanshuang Chen and Chuansheng Shen

Physica A: Statistical Mechanics and its Applications, 2015, vol. 424, issue C, 97-104

Abstract: We study the metastability and nucleation of the Blume–Capel model on complex networks, in which each node can take one of three possible spin variables {−1,0,1}. We consider the external magnetic field h to be positive, and let the chemical potential λ vary between −h and h in a low temperature, such that the 1 configuration is stable, and −1 configuration and/or 0 configuration are metastable. Combining the heterogeneous mean-field theory with simulations, we show that there exist four regions with distinct nucleation scenarios depending on the values of h and λ: the system undergoes a two-step nucleation process from −1 configuration to 0 configuration and then to 1 configuration (region I); nucleation becomes a one-step process without an intermediate metastable configuration directly from −1 configuration to 1 configuration (region II(1)) or directly from 0 configuration to 1 configuration (region II(2)) depending on the sign of λ; the metastability of the system vanishes and nucleation is thus irrelevant (region III). Furthermore, we show that in the region I nucleation rates for each step intersect that results in the occurrence of a maximum in the total nucleation rate.

Keywords: Nucleation; Complex networks; Metastable; Blume–Capel model; Heterogeneous mean-field theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:424:y:2015:i:c:p:97-104

DOI: 10.1016/j.physa.2015.01.015

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