A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields

¹ Institut für Physik, WA331, Johannes Gutenberg-Universität 55099 Mainz, Germany
² Institute for Physical Chemistry, Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
³ Department of Physics, University of Wisconsin-Madison 1150 University Avenue, Madison, WI 53706-1390, USA

Received: 1 February 2005
Accepted: 18 March 2005

Abstract

We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension . Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit , the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.