Interface-Roughening Phase Diagram of the Three-Dimensional Ising Model for All Interaction Anisotropies from Hard-Spin Mean-Field Theory

TL;DR

This paper maps the roughening phase diagram of the three-dimensional anisotropic Ising model across all interaction anisotropies using hard-spin mean-field theory, revealing how roughening and ordering transitions behave with anisotropy.

Contribution

It provides the first comprehensive phase diagram for the 3D anisotropic Ising model's roughening transitions across all anisotropies using a novel theoretical approach.

Findings

Roughening transition temperatures stabilize after the isotropic point.

Ordering transition temperature diverges with increasing anisotropy.

No roughening transition occurs in the 2D Ising model.

Abstract

The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.