J. Phys. I France
Volume 4, Numéro 11, November 1994
Page(s) 1597 - 1617
DOI: 10.1051/jp1:1994210
J. Phys. I France 4 (1994) 1597-1617

Ferrimagnetism in a disordered Ising model

Giovanni Paladin1, Michele Pasquini1 and Maurizio Serva2

1  Dipartimento di Fisica, Università dell' Aquila, 1-67100 Coppito, L'Aquila, Italy
2  Dipartimento di Matematica, Università dell' Aquila, 1-67100 Coppito, L'Aquila, Italy

(Received 20 May 1994, accepted 3 August 1994)

We introduce a one dimensional Ising model with two competing interactions : nearest neighbor random couplings $\pm J$ with equal probability and a positive infinite range coupling $\Lambda$. At low temperature T the model exhibits a first order phase transition between a ferromagnetic state (with magnetization m1 = 1 at T = 0) and a " ferrimagnetic " state (with m2= 2/3 at T = 0), when the disorder strength $J/ \Lambda$ is increased. For 5/12 $<J/\Lambda < 1$, a whole spectrum of ferrimagnetic ground states with magnetization mn = 2/(n + 1) ( n = 2, $\cdots$, $\infty$) is present while for $J/\lambda >1$ the ground state is given by a trivial one dimensional spin glass with m = 0. The main qualitative features of the model can be described by a simplified annealed model where the random couplings can arrange themselves to minimize free energy with the constraint that the number of positive couplings is fixed by the law of large numbers in the thermodynamic limit. This model is exactly solved at all temperatures and the diagram of phase is calculated.

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