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Simple physics of the partly pinned fluid systems

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.