# Critical phenomena at edges and corners

Pleimling, M. and Selke, W.
Institut für Theoretische Physik, Technische Hochschule Aachen,
D-52056 Aachen, Germany

### Abstract:

Using Monte Carlo techniques, the critical behaviour at edges and corners of the three-dimesional Ising model is studied. In particular, the critical exponent \beta_2 of the local magnetization at edges formed by two intersecting free surfaces is estimated to be, as a function of the opening angle \theta, 0.96 \pm 0.02 for \theta = 135^o, 1.28 \pm 0.04 for 90^o, and 2.30 \pm 0.10 for 45^o. The critical exponent \beta_3 of the corner magnetization of a cube is found to be 1.86 \pm 0.06. The Monte Carlo estimates are compared to results of mean field theory, renormalization group calculations, and high temperature series expansions.