  In this paper, we consider some aspects of the physics of the partly pinned
(PP) systems obtained by freezing in place particles in equilibrium bulk fluid
configurations in the normal (nonglassy) state. We first discuss the
configurational overlap and the disconnected density correlation functions,
both in the homogeneous and heterogeneous cases, using the tools of the theory
of adsorption in disordered porous solids. The relevant Ornstein-Zernike
equations are derived, and asymptotic results valid in the regime where the
perturbation due to the pinning process is small are obtained. Second, we
consider the homogeneous PP lattice gas as a means to make contact between
pinning processes in particle and spin systems and show that it can be
straightforwardly mapped onto a random field Ising model with a strongly
asymmetric bimodal distribution of the field. Possible implications of these
results for studies of the glass transition based on PP systems are also
discussed.
