Local functional models of critical correlations in thin films

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Critical Phenomena

Background:

• Local functional theories offer a powerful framework for understanding critical inhomogeneous fluids and magnets.
• These theories have shown promise in describing universal finite-size effects in critical thin films, including excess free energy and one-point function scaling.

Purpose of the Study:

• To extend local functional theories for predicting the two-point correlation function (G) in critical thin films with symmetric surface fields.
• To investigate the behavior of G in arbitrary dimensions (d).

Main Methods:

• Application of local functional theories to critical thin films.
• Comparison with conformal invariance predictions in d=2.
• Numerical predictions and derivation of analytical expressions for universal properties in d=3 and d>=4.

Main Results:

• Exact agreement with conformal invariance for correlation lengths (xi((n))) and asymptotic decay of G in d=2.
• New numerical predictions for universal finite-size correlation length and scaling functions in d=3 and d>=4.
• Derivation of highly accurate analytical closed-form expressions for universal properties in arbitrary dimensions.

Conclusions:

• Local functional theories provide a robust and versatile tool for analyzing critical phenomena in thin films across various dimensions.
• The study validates the theory in 2D and extends its predictive power to higher dimensions, offering new insights into the structure of the two-point correlation function.