The European Physical Journal B (EPJ B)

Eur. Phys. J. B 5, 805-810

Critical phenomena at edges and corners

M. Pleimling - W. Selke

Institut für Theoretische Physik, Technische Hochschule, 52056 Aachen, Germany

Received: 29 January 1998 / Accepted: 17 March 1998

Abstract
Using Monte-Carlo techniques, the critical behaviour at edges and corners of the three-dimensional 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 $\theta = 135^{\rm o}$ , $1.28 \pm 0.04$ for $90^{\rm o}$ , and $2.30 \pm 0.10$ for $45^{\rm o}$ . 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.

PACS
05.50.+q Lattice theory and statistics; Ising problems - 68.35.Rh Phase transitions and critical phenomena - 75.40.Mg Numerical simulation studies

Author for correspondance: selke@physik.rwth-aachen.de

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