Ferrimagnetic Blume-Emery-Griffiths sawtooth chain: Spin ice and quasiordering

The ferrimagnetic Blume-Emery-Griffiths one-dimensional model on the sawtooth chain with bilinear and biquadratic interactions between spins is studied exactly. Conditions at which the characteristic feature of spin ices, the remnant entropy at zero magnetic field appears, are studied. On the other hand, we determine at which set of parameters the model manifests quasiordering. That quasiordering reveals itself in almost nondecaying correlation functions below the quasicritical temperature, the jumplike temperature behavior of the entropy, and the quasipeculiarity in the temperature behavior of the specific heat at the quasicritical temperature. We show that the temperature behavior of magnetic moments of spins and the total magnetization drastically change its properties at the quasicritical temperature. The magnetic Grüneisen parameter manifests the most dramatic changes at the temperature of the quasiordering if the latter exists and in the ground state otherwise.