Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Surface Science

Background:

• Understanding wetting phenomena is crucial in various physical and chemical processes.
• The two-dimensional Ising model provides a fundamental framework for studying phase transitions.
• Previous studies often simplified surface interactions, limiting the scope of wetting phase diagrams.

Purpose of the Study:

• To determine the global phase diagram of wetting in the two-dimensional Ising model.
• To investigate the impact of enhanced surface coupling on wetting transitions.
• To analyze the behavior of surface thermodynamic quantities in different regimes.

Main Methods:

• Exact calculation of surface excess free energy.
• Inclusion of both surface field and surface-coupling enhancement.
• Analysis of the wetting transition order and critical region behavior.

Main Results:

• The wetting transition is second-order for finite surface coupling (J_{s}/J) and first-order as J_{s}/J approaches infinity.
• A practically invisible critical region exists for J_{s}/J≫1.
• A distinct preasymptotic regime shows first-order wetting behavior with anomalous scaling (exponent 3/2) for surface susceptibility and specific heat.

Conclusions:

• The global wetting phase diagram is complex, with distinct regimes influencing transition characteristics.
• Anomalous scaling in the preasymptotic regime offers new insights into surface critical phenomena.
• The findings challenge numerical studies in certain parameter ranges and highlight the importance of exact calculations.