ar X iv : c on d - m at / 0 10 84 18 v 1 2 7 A ug 2 00 1 Phase transitions at surfaces , edges , and corners

Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and corner critical exponents are non-universal and depend on the details of the model. The results obtained at the surface transition are compared to exact findings on critical two-dimensional Ising models with different types of defect lines.