Nucleation of a three-state spin model on complex networks

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 lambda 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 lambda: 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 lambda; 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. (C) 2015 Elsevier B.V. All rights reserved.