Critical behaviour of the restricted primitive model

Abstract

We study a critical behaviour of systems dominated by Coulombic interaction. For thispurpose we use the method of collective variables with a reference system. Starting fromthe Hamiltonian of the restricted primitive model (RPM), the simplest model of ionicfluids, we obtain a functional of the grand partition function given in terms of the twotypes of collective variable describing fluctuations of the total number density and thecharge density, respectively. As the result of integration over the charge density variables, amicroscopic based effective Hamiltonian of the RPM in the vicinity of its gas–liquid criticalpoint is constructed. Coefficients of the effective Hamiltonian describing the densityfluctuations near the gas–liquid critical point are analysed. It is shown that in spite of thelong-range character of the Coulombic potential the effective interactions appearing at thislevel of the description have a short-range character. Consequently, the effectiveHamiltonian obtained for the RPM in the vicinity of the critical point is in theform of the Ginzburg–Landau–Wilson Hamiltonian of an Ising-like model in amagnetic field. This confirms the fact that the critical behaviour of the RPM nearthe gas–liquid critical point belongs to the universal class of a 3D Ising model.