Asymmetric Fluid Criticality I: Scaling with Pressure Mixing

The thermodynamic behavior of a fluid near a vapor-liquid and, hence, asymmetric critical point is discussed within a general ``complete'' scaling theory incorporating pressure mixing in the nonlinear scaling fields as well as corrections to scaling. This theory allows for a Yang-Yang anomaly in which \mu_{\sigma}^{\prime\prime}(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when T\to T_{\scriptsize c}; it also generates a leading singular term, |t|^{2\beta}, in the coexistence curve diameter, where t\equiv (T-T_{\scriptsize c}) /T_{\scriptsize c}. The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which \chi^{(k)}\equiv \chi(\rho,T)/\rho^{k} (with \chi = \rho^{2} k_{\scriptsize B}TK_{T}) and C_{V}^{(k)}\equiv C_{V}(\rho,T)/\rho^{k} are maximal at fixed T, is carefully elucidated. These results are useful for analyzing simulations and experiments, since particular, nonuniversal values of k specify loci that approach the critical density most rapidly and reflect the pressure-mixing coefficient. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte. For comparison, a discussion of the classical (or Landau) theory is presented briefly and various interesting loci are determined explicitly and illustrated quantitatively for a van der Waals fluid.Comment: 21 pages in two-column format including 8 figure

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Turbidity data of weightless SF6 near its liquid-gas critical point

Light transmission measurements performed in SF6 close to its liquid–gas critical point are used to obtain turbidity data in the reduced temperature range..