Trigonometric models for scaling behavior near criticality
- 1 June 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 59 (22) , 14533-14545
- https://doi.org/10.1103/physrevb.59.14533
Abstract
Parametric scaling representations of the asymptotic equation of state, correlation lengths, and singular part of the Helmholtz free energy in the critical region of a system with a scalar order parameter are considered with the aim of fitting all 15 available independent universal amplitude ratios and describing naturally van der Waals loops. Defects in previous linear and cubic models and their extensions are described: they cannot represent analytically connected van der Waals loops or approximate satisfactorily all the known amplitude ratios. However, novel trigonometric parametric models for the free energy (and correlations) meet all the desiderata as demonstrated by the explicit numerical data presented.Keywords
This publication has 16 references indexed in Scilit:
- The shape of the van der Waals loop and universal critical amplitude ratiosJournal of Physics A: General Physics, 1998
- Fluid interface tensions near critical end pointsPhysical Review Letters, 1990
- Universality and interfaces at critical end pointsPhysical Review Letters, 1990
- Noncritical interface near a critical end point IIPhysica A: Statistical Mechanics and its Applications, 1980
- Critical Scattering in a Field and BelowPhysical Review Letters, 1973
- Correlation Between Critical Coefficients and Critical ExponentsPhysical Review Letters, 1969
- Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical PointThe Journal of Chemical Physics, 1969
- Parametric Representation of the Equation of State Near A Critical PointPhysical Review Letters, 1969
- The theory of equilibrium critical phenomenaReports on Progress in Physics, 1967
- Free Energy of a Nonuniform System. I. Interfacial Free EnergyThe Journal of Chemical Physics, 1958