Critical correlations and susceptibilities in the random-field spherical model

We investigate the behavior of the correlation function and the susceptibility of the random-field spherical model at the critical point. In particular we calculate the critical exponents {η} and {η}{} describing the divergences of the susceptibility and its disconnected part, respectively. In the case of short-range interactions we obtain {η}={η}{}=0. For power-law interactions Uᵢⱼ{~}rᵢⱼ^-σ we find {η}=1/2{η}{}=D+2-{σ} (for DD+2), where D is the spatial dimension. The Schwartz-Soffer exponent inequality {η}{}{≤}2{η} is satisfied and becomes an equality independent of the functional form of the interaction.