ZEROS ON THE TEMPERATURE AXIS OF SPIN CORRELATIONS IN A RANDOM BOND ISING CHAIN

We study the correlation between two spins diametrically opposite in a random Ising loop of 2r spins with random nearest-neighbour couplings. As a function of the inverse temperature beta, this correlation undergoes random sign changes with a density rho-r(beta). We determine this density for an arbitrary distribution P(K) of the coupling constants for (i) r --> infinity and (ii) the scaling limit beta --> infinity, r --> infinity at r/beta fixed. For --> infinity, the the total number of zeros on the beta-axis grows asymptotically as [GRAPHICS] As an application, the density of zeros is calculated for the spin-spin correlation in a double infinite Ising chain with random bonds, having, with a probability p, an infinite transverse coupling between each pair of corresponding sites. A connection is made with prediction from spin glass theory.