Ising chain with random short- and long-range interactions

An tract solution is obtained for the 1D Ising model, closed chain, with random short-and long-range interactions satisfying bimodal annealed distributions. The long-range interactions satisfy a strongly correlated distribution, and the distribution of the short-range interactions J(i) is explicitly given by (sic)(J(i)) = p delta(J(i)-J(A)) + (1 - p)delta(J(i) - J(B)). For the particular case of uniform ferromagnetic long-range interactions explicit results ale presented for the thermodynamic functions. It is shown that for dilute antiferromagnetic or for competing short-range interactions the spontaneous magnetization of the system can increase with temperature. It is also shown that the magnetization, as a function of temperature, can exhibit discontinuities. in addition to the usual first-and second-order phase transitions shown by the pure model (p = 0 or 1). (C) 1998 Elsevier Science B.V. All rights reserved.