Cluster Size in Random Mixtures and Percolation Processes

It is pointed out that the topological problem which arises in the theory of critical concentration in ferromagnetic crystals, and discussed recently by Elliott et al., is identical with a problem arising in the statistical theory of random mixtures. Additional terms of series expansions are given, and these enable improved estimates of the critical concentration to be made. A distinction is drawn between "site mixtures" and "bond mixtures," the latter having been previously considered under the heading of "percolation processes." The critical concentrations for the two problems are usually different. Some rigorous results regarding the critical concentrations are quoted.