Spin glass stiffness in zero dimensions

A unique analytical result for the Migdal–Kadanoff hierarchical lattice is obtained. The scaling of the defect energy for a zero-dimensional spin glass is derived for a bond distribution that is continuous at the origin. The value of the 'stiffness' exponent in zero dimensions, y₀ = −1, corresponds to the value also found in one dimension. This result complements and completes earlier findings for y_d at d > 0.