Edge critical behavior at the surface transition of Ising magnets
  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. 
M. Pleimling and W. Selke