https://doi.org/10.1007/s100510050506
Critical phenomena at edges and corners*
Institut für Theoretische Physik, Technische Hochschule,
52056 Aachen, Germany
Corresponding author: a selke@physik.rwth-aachen.de
Received:
29
January
1998
Accepted:
17
March
1998
Published online: 15 October 1998
Using Monte-Carlo techniques, the critical behaviour at
edges and corners of the three-dimensional Ising model is
studied. In particular, the critical exponent
of the local magnetization
at edges formed by two intersecting free surfaces is
estimated to be, as a function of the opening angle
θ, 
for 
,
for 
, and 
for 
. The critical exponent 
of
the corner magnetization of a cube is found to be
. The Monte-Carlo estimates are compared
to results of mean field theory, renormalization group
calculations and high temperature series expansions.
PACS: 05.50.+q – Lattice theory and statistics; Ising problems / 68.35.Rh – Phase transitions and critical phenomena / 75.40.Mg – Numerical simulation studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
