Problems involving percolation in liquids (i.e., involving connectivity of some sort) range from the metal–insulator transition in liquid metals to the properties of supercooled water. A common theme, however, is that connectivity can be distinguished from interaction and that one should not be slighted in order to describe the other. In this paper we suggest a model for percolation in liquids—the model of extended spheres—which permits connectivity to be studied in the context of, but independently from, liquid structure. This model is solved exactly in the Percus–Yevick approximation, revealing the existence of an optimum liquid structure for percolation. We analyze this behavior by first deriving an explicit diagrammatic representation of the Percus–Yevick theory for connectivity and then studying how the various diagrams contribute. The predictions are in excellent qualitative agreement with recent Monte Carlo calculations.

The general role of interparticle interactions is considered for percolation problems in liquids. With the aid of a diagrammatic formulation of the Percus-Yevick approximation, we analyze the dependence of connectedness (percolation) on correlation (interaction). This idea is illustrated by the analytical solution of the Percus-Yevick equation for a model of percolation in liquids, revealing that excluded volume (for example) may either enhance or suppress percolation.

This paper presents a new class of models capable of producing modulated order with solely nearest-neighbor forces. These deformable lattic-e models create modulated phases out of the interaction between spin and elastic degrees of freedom through a polarization, or feedback, mechanismas opposed to the purely spin or purely elastic models that employ either competing force or competing periodicity mechanisms. We show that one of the deformable-lattice models, in particular, can be formally reduced to the axial-next-nearest-neighbor Ising (ANNNI) model. This observation turns out to imply, first, that the ANNNI model can be regarded as an ordinary Ising model with a distribution of coupling constants (a random magnet), and second, that other spin models might be profitably thought of not as Hamiltonians, but as potentials of mean force resulting from integrating out elastic degrees of freedom. The possible implications are considered for both the range and nature of the interaction between chemisorbed species as well as that between intercalates in graphite.