Upton, P. J.
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|DOI (Digital Object Identifier) Link:||http://doi.org/10.1023/A:1013965806342|
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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|
|Extra Information:||The original publication is available at www.springerlink.com|
|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
|Depositing User:||Paul Upton|
|Date Deposited:||07 Jul 2006|
|Last Modified:||24 Feb 2016 11:12|
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