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The exact interface model for wetting in the two-dimensional Ising model

Upton, P. J. (2002). The exact interface model for wetting in the two-dimensional Ising model. International Journal of Thermophysics, 23(1) pp. 1–13.

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We use exact methods to derive an interface model from an underlying microscopic model, i.e., the Ising model on a square lattice. At the wetting transition in the two-dimensional Ising model, the long Peierls contour (or interface) gets depinned from the substrate. Using exact transfer-matrix methods, we find that on sufficiently large length scales (i.e., length scales sufficiently larger than the bulk correlation length) the distribution of the long contour is given by a unique probability measure corresponding to a continuous ``interface model". The interface binding ``potential" is a Dirac delta function with support on the substrate and, therefore, a distribution rather than a function. More precisely, critical wetting in the two-dimensional Ising model, viewed on length scales sufficiently larger than the bulk correlation length, is described by a reflected Brownian motion with a Dirac δ perturbation on the substrate so that exactly at the wetting transition the substrate is a perfectly reflecting surface, otherwise there exists a δ perturbation. A lattice solid-on-solid model was found to give identical results (albeit with modified parameters) on length scales sufficiently larger than the lattice spacing, thus demonstrating the universality of the continuous interface model.

Item Type: Journal Article
Copyright Holders: 2002 Plenum Publishing Corporation
ISSN: 0195-928X
Extra Information: The original publication is available at
Keywords: critical wetting; exact results; interface models; Ising models; solid-on-solid models.
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
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Item ID: 4495
Depositing User: Paul Upton
Date Deposited: 07 Jul 2006
Last Modified: 24 Feb 2016 11:12
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