International Journal of Thermophysics

, Volume 23, Issue 1, pp 1–13 | Cite as

The Exact Interface Model for Wetting in the Two-Dimensional Ising Model

  • P. J. Upton


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.

critical wetting exact results interface models Ising models solid-on-solid models 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • P. J. Upton
    • 1
  1. 1.H. H. Wills Physics Laboratory, University of BristolBristolUnited Kingdom

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