Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations

Details Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations

2003-06-12

arxiv.org/abs/cond-mat/0306331v1

Phys. Rev. E 68, 041506 (2003)

Physics

Condensed Matter

Statistical Mechanics

23 pages in the two-column format (including 13 figures) This is Part II of the previous paper [arXiv:cond-mat/0212145]

Scientific paper

10.1103/PhysRevE.68.041506

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.

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