Eur. Phys. J. B 64, 499-503 (2008)
https://doi.org/10.1140/epjb/e2008-00021-5

Phase transitions and interface fluctuations in double wedges and bi-pyramids with competing surface fields

¹ Institut für Theoretische Physik, Georg-August Universität, 37073 Göttingen, Germany
² Institute for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
³ Institut für Physik, WA 331, Johannes Gutenberg Universität, 55099 Mainz, Germany
⁴ Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602-2451, USA

Corresponding author: ^a mmueller@theorie.physik.uni-goettingen.de

Received: 27 August 2007
Revised: 7 November 2007
Published online: 18 January 2008

Abstract

The interplay between surface and interface effects on binary AB mixtures that are confined in unconventional geometries is investigated by Monte Carlo simulations and phenomenological considerations. Both double-wedge and bi-pyramid confinements are considered and competing surface fields are applied at the two opposing halves of the system. Below the bulk critical temperature, domains of opposite order parameter are stabilized at the corresponding corners and an interface runs across the middle of the bi-partite geometry. Upon decreasing the temperature further one encounters a phase transition at which the AB symmetry is broken. The interface is localized in one of the two wedges or pyramids, respectively, and the order parameter is finite. In both cases, the transition becomes discontinuous in the thermodynamic limit but it is not a first-order phase transition. In an antisymmetric double wedge geometry the transition is closely related to the wedge-filling transition. Choosing the ratio of the cross-section of the wedge and its length L_y according to const., simulations and phenomenological consideration show that the new type of phase transition is characterized by critical exponents , , and for the specific heat, order parameter, and susceptibility, respectively. In an antisymmetric bi-pyramid the transition occurs at the cone-filling transition of a single pyramid. The important critical fluctuations are associated with the uniform translation of the interface and they can be described by a Landau-type free energy. Monte Carlo results provide evidence that the coefficients of this Landau-type free energy exhibit a system-size dependence, which gives rise to critical amplitudes that diverge with system size and result in a transition that becomes discontinuous in the thermodynamic limit.