Sensitivity to boundary conditions of Ising spin-glasses

Results of numerical investigations of the scaling properties of the equilibrium sensitivity to changes in the boundary conditions in two random two-dimensional Ising systems at $T=0\mathrm{}$ are presented. The spin-glass with a Gaussian distribution of exchange couplings is characterized by an algebraic-size dependence of this sensitivity. The results may be interpreted to yield a lower critical dimensionality of 4 for this system. For the system with a $\pm J$ probability distribution for the exchange couplings we expect an exponential-size dependence of the sensitivity but our data are inconclusive.