Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations

TL;DR

This paper develops finite-size scaling theory for asymmetric fluids near criticality, focusing on simulation boundary conditions, and demonstrates its application to specific models, confirming Ising-type behavior.

Contribution

It extends the complete thermodynamic scaling theory to finite systems, incorporating pressure mixing and corrections, and applies it to estimate critical parameters in fluid models.

Findings

Finite-size scaling loci help estimate critical temperature and density.

The theory confirms Ising universality class for studied models.

Application to models yields estimates consistent with known critical exponents.

Abstract

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions, $L$, focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded ``complete'' thermodynamic $(L\to\infty)$ scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling ${[arXiv:cond-mat/0212145]}$, is extended to finite $L$, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when $L\to\infty$, the second temperature derivative, $(d^{2}\mu_{\sigma}/dT^{2})$, of the chemical potential along the phase boundary, $\mu_{\sigma}(T)$, diverges when $T\to\Tc -$. The finite-size behavior of various special {\em critical loci} in the temperature-density or $(T,\rho)$ plane, in particular, the $k$-inflection susceptibility loci and the $Q$-maximal loci -- derived from $Q_{L}(T,<\rho>_{L}) \equiv < m^{2}>^{2}_{L}/< m^{4}>_{L}$ where $m \equiv \rho - <\rho>_{L}$ -- is carefully elucidated and shown to be of value in estimating $\Tc$ and $\rhoc$. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent $\nu$ that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.