### 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) |
---|---|

Pages (from-to) | 1097-1111 |

Number of pages | 15 |

Journal | Journal of Statistical Physics |

Volume | 63 |

Issue number | 5-6 |

DOIs | |

State | Published - Jun 1991 |

### Fingerprint

### Keywords

- Ising model
- monolayer
- random surface
- Wetting

### ASJC Scopus subject areas

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

### Cite this

*Journal of Statistical Physics*,

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

**The wetting transition in a random surface model.** / Abraham, D. B.; Newman, Charles.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 63, no. 5-6, pp. 1097-1111. https://doi.org/10.1007/BF01030001

}

TY - JOUR

T1 - The wetting transition in a random surface model

AU - Abraham, D. B.

AU - Newman, Charles

PY - 1991/6

Y1 - 1991/6

N2 - 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 Tw 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, Tw is independent of b and there is a logarithmic specific heat divergence as Tw is approached from either side. Here we show that for b<0, Tw 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<Tw.

AB - 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 Tw 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, Tw is independent of b and there is a logarithmic specific heat divergence as Tw is approached from either side. Here we show that for b<0, Tw 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<Tw.

KW - Ising model

KW - monolayer

KW - random surface

KW - Wetting

UR - http://www.scopus.com/inward/record.url?scp=0009069988&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009069988&partnerID=8YFLogxK

U2 - 10.1007/BF01030001

DO - 10.1007/BF01030001

M3 - Article

VL - 63

SP - 1097

EP - 1111

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -