Surface coupling effect on wetting and layering transitions

TL;DR

This study investigates how surface coupling influences the layering transition temperature in a spin-1/2 Ising film, revealing complex dependencies on film thickness, surface magnetic field, and coupling strength using mean field theory.

Contribution

It introduces a detailed analysis of the surface coupling effect on layering transitions, identifying critical values and behaviors not previously characterized.

Findings

For $J_s > J_{sc}$, $T_L$ decreases with $N$.

Three distinct behaviors of $T_L$ depending on $H_s$ and $N$.

Wetting temperature $T_w$ can be higher or lower than the layering transition temperature.

Abstract

The effect of the surface coupling $J_s$ on the dependency of the layering transition temperature $T_L$ as a function of the thickness $N$, of a spin-1/2 Ising film, is studied using the mean field theory. It is found that for $J_s$ greater than a critical value ($J_{sc}=1.30$), the layering transition temperature decreases when the film thickness $N$ increases for any values of the surface magnetic field $H_s$. While, for $J_s < J_{sc}$, the behaviour of the layering transition temperature $T_L$, as a function of $N$, depends strongly on the values of $H_s$. Indeed, we show the existence of three distinct behaviours of $T_L$, as a function of the film thickness $N$, separated by two critical surface magnetic fields $H_{sc1}$ and $H_{sc2}$, namely: $(i)$ for $H_s < H_{sc1}$, $T_L$ increases with $N$; $(ii)$ for $H_{sc1} < H_s < H_{sc2}$, $T_L$ increases for small values of $N$, and decreases for large value ones; (iii) while for $H_s > H_{sc2}$, $T_L$ decreases with increasing the film thickness. Furthermore, depending on the values of $J_s$, the wetting temperature $T_w (T_w=T_L$ when $N \to \infty$ for a given material), can be greater or smaller than the layering transition temperature of a film of thickness $N$ of the same material.