### Abstract

We continue our analysis of the phase diagram of a discrete random surface, with no "downward fingers," lying above a flat two-dimensional substrate. The surface is closely related to the 2D Ising model and its free energy is exactly solvable in much (but not all) of the phase diagram. There is a transition at temperature T_{w} from a high-T infinite height or wet phase to a low-T finite height or partially wet phase. Previously it was shown that when a parameter b, related to the contact interaction, is positive, T_{w} is independent of b and there is a logarithmic specific heat divergence as T_{w} is approached from either side. Here we show that for b<0, T_{w} does depend on b and there is no thermodynamic singularity from the wet phase. The partially wet phases for b≤0 and b>0 differ in the absence or presence of a monolayer covering the entire substrate; this results in a first-order transition across the line b=0, T<T_{w}.

Original language | English (US) |
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Pages (from-to) | 1097-1111 |

Number of pages | 15 |

Journal | Journal of Statistical Physics |

Volume | 63 |

Issue number | 5-6 |

DOIs | |

State | Published - Jun 1 1991 |

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### Keywords

- Ising model
- Wetting
- monolayer
- random surface

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*63*(5-6), 1097-1111. https://doi.org/10.1007/BF01030001