Re-entrant phase transitions of the Blume-Emery-Griffiths model

Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

“…In closing this paper we want to mention that the antiferromagnetic Ising model is equivalent to a spin-one Ising model [41]. Our result confirms that a re-entrant phase transition occurs in the latter on the simple cubic lattice.…”

Critical activity of the hard-sphere lattice gas on the body-centred cubic lattice

“…In closing this paper we want to mention that an antiferromagnetic Ising model in an external field is equivalent to a Blume-Emery-Griffiths model [26]. Kasono and Ono [27] confirms that there is a re-entrant phase transition of the latter on the body-centred cubic lattice. Our result supports theirs with high precision.…”

Low Temperature Properties of the Blume–emery–griffiths (Beg) Model in the Region With an Infinite Number of Ground State Configurations

“…In recent works, using Mean Field, Monte Carlo and approximate renormalization group techniques, phase diagrams have been found to have a very rich structure [2][3][4][5][6]. Rigorous results have been obtained in [7], where the number of pure phases for the 2-d model has been obtained using a generalized Pirogov-Sinai theory (for the standard theory, see [8]), and in [9,10], where the two-point function is studied by correlation inequality techniques.…”