Nucleation of a three-state spin model on complex networks

Abstract

h i g h l i g h t s• Nucleation of a three-state spin model on complex networks is studied.• Heterogeneous mean-field theory is developed for evaluating free-energy barrier.• Four regions are distinguished as distinct nucleation scenarios. • A maximal nucleation rate is found at the two-step nucleation region. a b s t r a c tWe 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 meanfield 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.

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