Extension of global renormalization group theory to include symmetric and asymmetric fluctuations for critical phase behavior
Journal
Journal of Molecular Liquids
Journal Volume
438
Start Page
128721
ISSN
01677322
Date Issued
2025-11-15
Author(s)
Shih, Yen-Jen
Abstract
In this work, we develop a refined formulation of the Global Renormalization Group Theory (GRGT) that incorporates both symmetric and asymmetric composition fluctuations, referred to as GRGT-SAF. This new approach improves upon the original symmetric-only GRGT (GRGT-SF) by extending the integration domain to include all possible fluctuation patterns. Analytical expressions for the Gibbs free energy and internal energy are derived without introducing additional parameters. The GRGT-SAF method is validated using the three-dimensional Ising model on a cubic lattice, i.e., a standard reference for critical phenomena in binary mixtures. Results from Monte Carlo simulation for equilibrium compositions and critical point, and from high-temperature expansion for critical exponents are used for comparison. Our results shows that GRGT-SAF provides more accurate predictions of the critical temperature, critical amplitude, critical exponent γ, specific heat, and osmotic compressibility than GRGT-SF and the classical mean-field model. GRGT-SAF also better satisfies Rushbrooke's identity and shows faster convergence in both free energy iteration and phase equilibrium calculations. Owing to its robustness and accuracy, the GRGT-SAF formulation offers a promising route for describing phase behavior in real mixtures near the critical point.
Subjects
Composition fluctuation
Critical point
Local composition
Phase transition
Renormalization group theory
Publisher
Elsevier B.V.
Type
journal article