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

The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimo dal annealed distributions is studied. This generalizes the random model di scussed 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. A t low temperatures the system can exist in a 'ferrimagnetic' phase with mag netization 0 < sigma < 1, in addition to the usual paramagnetic, ferromagne tic and antiferromagnetic phases. For a fixed distribution of the random va riables the system presents up to three tricritical points for different in tensities of the long-range interactions. Field-temperature diagrams can pr esent up to four critical points. (C) 1999 Elsevier Science B.V. All rights reserved.