# 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.

cond-mat/9801320