FERRIMAGNETISM IN A DISORDERED ISING-MODEL

We introduce a one dimensional Ising model with two competing interact ions: nearest neighbor random couplings +/-J with equal probability an d a positive infinite range coupling Lambda. At low temperature T the model exhibits a first order phase transition between a ferromagnetic state (with magnetization m(1) = 1 at T = 0) and a << ferrimagnetic >> state (with m(2) = 2/3 at T = 0), when the disorder strength J/Lambda is increased. For 5/12 < J/Lambda < 1, a whole spectrum of ferrimagne tic ground states with magnetization m(n) = 2/(n + 1) (n = 2, ..., inf inity) 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 ene rgy 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 calcul ated.