### Abstract

A natural model of a discrete random surface lying above a two-dimensional substrate is presented and analyzed. An identification of the "level curves" of the surface with the Peierls contours of Ising spin configurations leads to an exactly solvable free energy, with logarithmically divergent specific heat. The thermodynamic critical point is shown to be a wetting transition at which the surface height diverges. This is so even though the surface has no "downward fingers" and hence no "entropic repulsion" from the substrate.

Original language | English (US) |
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Pages (from-to) | 181-200 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 125 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1989 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*125*(1), 181-200. https://doi.org/10.1007/BF01217776

**Surfaces and Peierls contours : 3-d wetting and 2-d Ising percolation.** / Abraham, D. B.; Newman, Charles.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 125, no. 1, pp. 181-200. https://doi.org/10.1007/BF01217776

}

TY - JOUR

T1 - Surfaces and Peierls contours

T2 - 3-d wetting and 2-d Ising percolation

AU - Abraham, D. B.

AU - Newman, Charles

PY - 1989/3

Y1 - 1989/3

N2 - A natural model of a discrete random surface lying above a two-dimensional substrate is presented and analyzed. An identification of the "level curves" of the surface with the Peierls contours of Ising spin configurations leads to an exactly solvable free energy, with logarithmically divergent specific heat. The thermodynamic critical point is shown to be a wetting transition at which the surface height diverges. This is so even though the surface has no "downward fingers" and hence no "entropic repulsion" from the substrate.

AB - A natural model of a discrete random surface lying above a two-dimensional substrate is presented and analyzed. An identification of the "level curves" of the surface with the Peierls contours of Ising spin configurations leads to an exactly solvable free energy, with logarithmically divergent specific heat. The thermodynamic critical point is shown to be a wetting transition at which the surface height diverges. This is so even though the surface has no "downward fingers" and hence no "entropic repulsion" from the substrate.

UR - http://www.scopus.com/inward/record.url?scp=1842565462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842565462&partnerID=8YFLogxK

U2 - 10.1007/BF01217776

DO - 10.1007/BF01217776

M3 - Article

VL - 125

SP - 181

EP - 200

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -