Abstract
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 < sigma < 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. (C) 1999 Elsevier Science B.V. All rights reserved.
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