Blume-Emery-Griffiths model on Random Graphs

TL;DR

This paper investigates the Blume-Emery-Griffiths model on random graphs, analyzing how average connectivity influences phase diagrams using replica symmetry and population dynamics, with results compared to mean field and renormalization group methods.

Contribution

It introduces a novel analysis of the BEG model on random graphs, deriving a self-consistent local field distribution and exploring connectivity effects on phase behavior.

Findings

Connectivity alters phase diagram topology.

Phase diagrams differ from mean field predictions.

Population dynamics effectively solves the model.

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.