Blume-Emery-Griffiths model on Random Graphs

Abstract

The Blume-Emery-Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica symmetry formalism of order parameter functions. A self-consistent equation for the distribution of local fields is derived and numerically solved by a population dynamics algorithm. The results show that the average connectivity amounts to changes in the topology of the phase diagrams. Phase diagrams for representative values of the model parameters are compared with those obtained for fully connected mean field and renormalization group approaches.

14 pages, 6 figures, accepted for publication in Physica A

References in corpus (3)

• Approximating the XY model on a random graph with a $q$-state clock model
• Phase transitions in the three-state Ising spin-glass model with finite connectivity
• Ising spin glass in a random network with a gaussian random field