Critical behavior of then-component cubic model and the Ashkin-Teller fixed line

The cubic lattice gas, a generalization of the n-component face-cubic model, is studied in two dimensions by variational renormalization-group techniques for general n, and by an exact mapping onto a solid-on-solid model for $n=2$. This approach reveals new interconnections among the class of cubic, Potts, and Ashkin-Teller phase-transition phenomena. In particular, it is shown that the fixed line of the Ashkin-Teller lattice gas serves as the backbone for a hierarchy of pairs of fixed points which branch off from it, as n is decreased from 2, at special points where two operators are marginal. The phase diagrams of the pure and dilute n-component cubic models are obtained and the orders of all transitions are determined. The cubic phase transition is found to be first order for all n>nc=2. The evolution of the results as a function of dimensionality is discussed briefly.