One-dimensional Ising model with long-range and random short-range interactions

• Published in: Journal of magnetism and magnetic materials Vol. 192; no. 1; pp. 177 - 190
• Main Authors: Vieira, A.P., Gonçalves, L.L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.1999; Elsevier Science
• Subjects: Classical spin models; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Exact sciences and technology; General theory and models of magnetic ordering; Long-range interactions; Magnetic properties and materials; One-dimensional model; Physics; Random Ising model; One-dimensional model; Long-range interactions; Random Ising model; Phase diagrams; Long range interaction; Spontaneous magnetization; Theoretical study; Ising model; Finite temperature; One-dimensional systems
• ISSN: 0304-8853
• DOI: 10.1016/S0304-8853(98)00362-X

The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by Paladin et al. (J. Phys. I France 4 (1994) 1597). Exact results are obtained for the thermodynamic functions at arbitrary temperatures, and special attention is given to the induced and spontaneous magnetization. At low temperatures the system can exist in a `ferrimagnetic’ phase with magnetization 0< σ<1, in addition to the usual paramagnetic, ferromagnetic and antiferromagnetic phases. For a fixed distribution of the random variables the system presents up to three tricritical points for different intensities of the long-range interactions. Field-temperature diagrams can present up to four critical points.