Non-Ising-like effects in the liquid-vapor transition: Equations of state

Abstract

A Landau-Ginzburg-Wilson model is derived for a single-component fluid whose particles interact via a two-body potential. The effective Hamiltonian contains both even and odd powers in the order parameter (local fluid density). We study the effect of quintic interactions absent in the Ising model, and characterized by a new exponent ${\phi }_5$, on various singular thermodynamic functions near the critical point. Mean-field, scaling, and renormalization-group (in $d=4-\epsilon$ dimensions) theories are used to evaluate the non-Ising effects due to ${\phi }_5$. One of the main results of the asymmetry in this model is that it produces the leading singularity of the liquid-vapor coexistence diameter near the critical point: ${\mathrm{}\left|t\right|\mathrm{}}^{\beta -{\phi }_5}$, where $\beta$ is the usual order-parameter exponent and $t$ is the reduced tem$\stackrel{\mathrm{̇}}{\mathrm{p}}$erature. The singularity ${\mathrm{}\left|t\right|\mathrm{}}^{1-\alpha }$ ($\alpha$ being the specific heat exponent) predicted by earlier phenomenological theories is not present in this theory. The problems associated with observing the non-Ising effects are briefly discussed.