Shih, Yen-JenYen-JenShihSHIANG-TAI LIN2025-11-272025-11-272025-11-1501677322https://www.scopus.com/record/display.uri?eid=2-s2.0-105020600029&origin=resultslisthttps://scholars.lib.ntu.edu.tw/handle/123456789/734180In 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.falseComposition fluctuationCritical pointLocal compositionPhase transitionRenormalization group theory[SDGs]SDG13journal article10.1016/j.molliq.2025.1287212-s2.0-105020600029