Magnetic and nonmagnetic glass transitions in the Blume–Emery–Griffiths model with competing biquadratic interactions (abstract)

Abstract

The Blume–Emery–Griffiths model, a spin-1 Ising model with bilinear (J), biquadratic (K), and crystal field (Δ) terms, provides a general system for the analysis of both density and magnetic fluctuations. Using a Monte Carlo hard-spin mean-field approach, we have calculated the phase diagrams resulting from a random bimodal distribution of biquadratic interactions, Kij=±K, with equal probabilities. The quenched disorder in K competes with the propagation of long-range magnetic order and leads to two types of glassy ordered phases, magnetic and nonmagnetic. The variance in the site density over the lattice serves as an order parameter for the transition to these glassy phases. We compare the structure and overlaps of their low lying energy states with those of the three-dimensional Ising spin glass, determined using the same method. The magnetic glass exhibits a much more gradual loss of overlap with its low-temperature state than the spin glass. The form of the overlap versus temperature curve in the vicinity of the critical temperature for the magnetic glass suggests that the system is fluctuating between a pair of ordered states, with one obtained from the other by flipping all spins, rather than sampling many different states.