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 $\left(\overrightarrow{L}\infty \right)$ scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling [Phys. Rev. E 67, 061506 (2003)] is extended to finite $L,$ initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when $\overrightarrow{L}\infty ,$ the second temperature derivative ${(d}^2{\mu }_{\sigma }{/dT}^2)$ of the chemical potential along the phase boundary ${\mu }_{\sigma }\mathrm{}\left(T\right)\mathrm{}$ diverges when $\overrightarrow{T}{T}_{\mathrm{c}}-.$ The finite-size behavior of various special critical loci in the temperature-density or $(T,\rho )$ plane, in particular, the k-inflection susceptibility loci and the Q-maximal loci — derived from $Q_L(T,〈\rho {〉}_L)\equiv 〈m^2{〉}_L^2/〈m^4{〉}_L$ where $m\equiv \rho -〈\rho {〉}_L$ — is carefully elucidated and shown to be of value in estimating $T_{\mathrm{c}}$ and ${\rho }_{\mathrm{c}}.$ 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.

• Received 16 June 2003

DOI:https://doi.org/10.1103/PhysRevE.68.041506