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The Exact Interface Model for Wetting in the Two-Dimensional Ising Model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Upton, P. J. |
| Copyright Year | 2002 |
| Abstract | 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. |
| Starting Page | 1 |
| Ending Page | 13 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1023/A:1013965806342 |
| Alternate Webpage(s) | http://oro.open.ac.uk/4495/1/ijtherm2s.pdf |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1023/A:1013965806342 |
| Alternate Webpage(s) | https://doi.org/10.1023/A%3A1013965806342 |
| Volume Number | 23 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
