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We present a model for systems of interacting superparamagnetic particles, based on a generalized version of the Preisach model of hysteresis that incorporates thermal overbarrier relaxation events. The model provides a physically transparent picture of processes like thermal blocking, field cooling (FC), and zero field cooling (ZFC). It is able to replicate the principal structural features of the FC and ZFC response observed in real superparamagnetic assemblies, as well as the systematic variations in this structure with changes in applied field and in the state of aggregation of the particles. The physical origins of these experimental systematics are discussed in terms of the characteristic coercive and interaction fields of the individual subsystems, and their distribution in the Preisach plane.