Universality class of the critical point in the restricted primitive model of ionic systems

TL;DR

This paper analyzes the critical behavior of the restricted primitive model of ionic systems, demonstrating its belonging to the Ising universality class through a detailed diagrammatic and field-theoretic approach.

Contribution

It derives an exact reduction to a one-field theory and establishes a correspondence between the RPM's critical behavior and the Ising universality class.

Findings

Charge-density correlation singularity is removed when fluctuations are included.

Diagram resummation yields regular expressions for correlation functions.

The model belongs to the Ising universality class.

Abstract

A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated ito disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.