Critical behavior of the Widom-Rowlinson mixture: coexistence diameter and order parameter

TL;DR

This study investigates the critical behavior of the Widom-Rowlinson mixture in three dimensions using grand canonical Monte Carlo simulations and finite size scaling, confirming Ising universality class critical exponents.

Contribution

It provides the first detailed analysis of the coexistence diameter and order parameter critical behavior in the Widom-Rowlinson mixture, highlighting the dominance of a specific singular term and small pressure-mixing effects.

Findings

Critical density measured as 0.7486 +/- 0.0002.

Critical exponents alpha, beta, and nu agree with 3D Ising universality.

No evidence of t^(2beta) term, indicating small pressure-mixing.

Abstract

The critical behavior of the Widom-Rowlinson mixture [J. Chem. Phys. 52, 1670 (1970)] is studied in d=3 dimensions by means of grand canonical Monte Carlo simulations. The finite size scaling approach of Kim, Fisher, and Luijten [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t^(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t^(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure-mixing in this model is small. The critical density is measured to be rho*sigma^3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d=3 Ising criticality.