Edge critical behavior at the surface transition of Ising magnets

TL;DR

This study investigates the critical behavior of edges in three-dimensional Ising models at surface transitions, revealing non-universal edge magnetization exponents influenced by local couplings.

Contribution

It demonstrates that at the surface transition, the edge magnetization exponent varies with local couplings, contrasting with the universal behavior at the ordinary transition.

Findings

Edge magnetization exponent is non-universal at the surface transition.

Exponents depend on edge and edge-surface couplings.

Comparison made with 2D Ising models with defects.

Abstract

Using Monte Carlo techniques, Ising models with ferromagnetic nearest-neighbor interactions on a simple cubic lattice are studied. At the surface transition, the critical exponent $\beta_2$ of the edge magnetization is found to be non-universal, depending on the edge and edge-surface couplings, in contrast to the situation at the ordinary transition. Results are compared to those for two-dimensional Ising magnets with chain and ladder defects.