Finite-size scaling analysis of exact ground states for +/-J spin glass models in two dimensions

With the help of exact ground states obtained by a polynomial algorithm we compute the domain wall energy Delta at zero temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the stability of the ferromagnetic and the spin glass order ceases to exist at a unique concentration p(c) for the ferromagnetic bonds. In the vicinity of this critical point, the size and concentration dependence of the first and second moment of the domain mall energy are, for both models, described by a common finite-size scaling form. Moreover, below this concentration the stiffness exponent turns out to be slightly negative, theta(S) = -0.056(6), indicating the absence of any intermediate spin glass phase at non-zero temperature.