Revised scaling variables in systems with many-body interactions

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Abstract
Thermodynamic perturbation theory and the Kirkwood-Salsburg correlation function identities are used to study nearest-neighbor lattice gases with certain weak symmetry-breaking many-body interactions. It is shown that such systems may be mapped onto symmetric models by the introduction of suitable effective interactions and a shifted chemical potential, both of which depend explicitly on the temperature and fugacity of the original model. In the critical region, such a thermodynamic-state dependence implies the existence of a thermal scaling field which depends on the bare chemical potential, and this ‘‘field mixing’’ leads to a breakdown in the classical law of the rectilinear diameter. These results give a microscopic interpretation to a field-theoretic renormalization-group analysis which derives such a diameter singularity from the presence of terms cubic and higher in the order parameter and its gradients in an asymmetric Landau-Ginzburg-Wilson Hamiltonian. For a primarily repulsive three-body potential like the Axilrod-Teller interaction in classical insulating fluids, and in comparison with recent experiments, the analysis correctly describes the observed trends in the critical and near-critical behavior of the diameters with increasing particle polarizability.