Phase transitions and critical phenomena of the Blume–Capel model in complex networks

This paper investigates the adsorption of gas molecules onto complex materials. We explore the mapping of the traditional soft-core lattice gas model to the Blume–Capel model, investigating the phase transition and critical phenomena of the Blume–Capel model on complex networks. Additionally, we discuss the impact of cross rewiring links on the network structure. Through Monte Carlo simulation, we obtain thermodynamic properties of different network structures and determine the critical temperatures of these quantities via finite-size analysis. The results reveal the following. As the control parameter r increases, the transition temperature increases. With an increase in the crystal field strength, the transition temperature decreases. Tri-critical phenomena are observed at various control parameters. Graphical abstract