EXACT GROUND-STATE ENERGY OF THE ISING SPIN-GLASS ON STRIPS

We propose a new method for exact analytical calculation of the ground -state energy of the Ising spin glass on strips. An outstanding advant age of this method over the numerical transfer matrix technique is tha t the energy is obtained for complex values of the probability describ ing quenched randomness. We study the +/-J and the site-random models using this method for strips of various sizes up to 5 x infinity. The ground-state energy of these models is found to have singular points i n the complex-probability plane, reminiscent of Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The +/-J Ising model ha s a series of singularities which may approach a limiting point around p similar to 0.9 on the real axis in the limit of infinite width.