Edge wetting of an Ising three-dimensional system

TL;DR

This study explores how edges influence wetting and layering transitions in a 3D Ising model, revealing temperature-dependent surface and bulk transitions, with findings supported by mean field theory and Monte Carlo simulations.

Contribution

It provides new insights into edge effects on wetting and layering transitions in a 3D Ising system, including temperature thresholds and transition types, using combined theoretical and simulation approaches.

Findings

Surface and bulk transitions depend on temperature and system size.

Monte Carlo results are lower than mean field predictions but converge at low temperatures.

Transitions are of first order, with critical temperatures decreasing with size and surface field.

Abstract

The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field (MF) theory and Monte Carlo (MC) simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely: surface and bulk transition, surface transition and bulk transition. However, there exist a surface intra-layering temperature $T_{L}^{s}$, above which the surface and the intra-layering surface transitions occur. While the bulk layering and intra-layering transitions appear above an other finite temperature $T_{L}^{b} (\ge T_{L}^{s})$. These surface and bulk intra-layering transitions are not seen in the perfect surfaces case. Numerical values of $T_{L}^{s}$ and $T_{L}^{b}$, computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. $T_{L}^{s}$ and $T_{L}^{b}$ decrease when increasing the system size and/or the surface magnetic field. In particular, $T_{L}^{b}$ reaches the wetting temperature $T_{w}$ for sufficiently large system sizes.