Soluble Model Fluids with Complete Scaling and Yang-Yang Features

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Physical Chemistry

Background:

• Compressible cell gas (CCG) models exhibit critical anomalies.
• Complete scaling and pressure mixing are key properties of these models.

Purpose of the Study:

• Investigate Yang-Yang (YY) and singular diameter critical anomalies in exactly soluble CCG models.
• Analyze the behavior of the C(μ) and density difference ρ(d)-ρ(c) near the critical point.
• Determine the factors influencing the YY ratio R(μ) = C(μ)/C(V).

Main Methods:

• Exact solution of CCG models with complete scaling and pressure mixing.
• Analysis of critical isochore behavior (ρ=ρ(c)).
• Examination of the impact of local CCG cell volume fluctuations on R(μ).

Main Results:

• C(μ) diverges as |t|^(-α) and ρ(d)-ρ(c) scales as |t|^(2β) on the critical isochore.
• Freely fluctuating cell volumes allow R(μ) to range from -∞ to 1/2.
• Anticorrelated free volumes are required for R(μ) > 0.

Conclusions:

• The YY ratio R(μ) is sensitive to the correlations of local cell volumes.
• Energy-volume coupling, as seen in decorated CCGs and water models, is relevant to R(μ).
• The study provides insights into critical phenomena in gas models.