Liquid-state methods for random media: Random sequential adsorption

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Abstract
A large number of statistical models of current interest in physics can be characterized as differentially quenched systems. They are prepared by successively introducing into a volume one fraction after another of the particles in a many-body system, each successive fraction being equilibrated while all the earlier fractions are kept frozen in place. Examples of current interest include self-avoiding walks, chemical association models, growth models, and models of random sequential adsorption (RSA). In this paper, we develop generalizations of the replica method adequate for calculating the properties of such systems. These are applied to RSA, resulting in both virial series and integral equations for the physical quantities describing this system. We extend the virial series for the adsorption rate to give excellent agreement with simulation results at all densities.