Thermodynamic properties of the random-field spherical model

The thermodynamic properties of a $d$-dimensional classical vector-spin system in a random magnetic field are calculated explicitly in the spherical-model limit. The system is characterized by significant spin-glass order of the Edwards-Anderson type even when no transition to a state with spontaneous magnetization occurs. This spin-glass order should result in observable effects in the magnetic susceptibility and specific heat. The properties of the random-field spherical model are compared with those reported for the corresponding Ising model. The behavior of the coherence length is identical in both models at their respective lower critical dimensionalities.