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 ${\mathit{U}}_{\mathit{i}\mathit{j}}$∼${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{-}\mathrm{\sigma }}$ we find η=1/2η¯=D+2-σ (for D<σ<D+2), where D is the spatial dimension. The Schwartz-Soffer exponent inequality η¯≤2η is satisfied and becomes an equality independent of the functional form of the interaction.

• Received 28 December 1993

DOI:https://doi.org/10.1103/PhysRevB.50.1272