### Abstract

We consider a class of d-dimensional Gaussian lattice field which is known as a model of semi-flexible membrane. We study the free energy of the model with external potentials and show the following: (1) We consider the model with δ-pinning and prove that the field is always localized when d≥4. (2) Consider the model confined between two hard walls. We give asymptotics of the free energy as the height of the wall goes to infinity.

Original language | English |
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Pages (from-to) | 18-34 |

Number of pages | 17 |

Journal | Journal of Statistical Physics |

Volume | 147 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Apr |

### Fingerprint

### Keywords

- Confinement
- Gaussian field
- Membrane
- Pinning

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**On the Free Energy of a Gaussian Membrane Model with External Potentials.** / Sakagawa, Hironobu.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 147, no. 1, pp. 18-34. https://doi.org/10.1007/s10955-012-0475-0

}

TY - JOUR

T1 - On the Free Energy of a Gaussian Membrane Model with External Potentials

AU - Sakagawa, Hironobu

PY - 2012/4

Y1 - 2012/4

N2 - We consider a class of d-dimensional Gaussian lattice field which is known as a model of semi-flexible membrane. We study the free energy of the model with external potentials and show the following: (1) We consider the model with δ-pinning and prove that the field is always localized when d≥4. (2) Consider the model confined between two hard walls. We give asymptotics of the free energy as the height of the wall goes to infinity.

AB - We consider a class of d-dimensional Gaussian lattice field which is known as a model of semi-flexible membrane. We study the free energy of the model with external potentials and show the following: (1) We consider the model with δ-pinning and prove that the field is always localized when d≥4. (2) Consider the model confined between two hard walls. We give asymptotics of the free energy as the height of the wall goes to infinity.

KW - Confinement

KW - Gaussian field

KW - Membrane

KW - Pinning

UR - http://www.scopus.com/inward/record.url?scp=84860384968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860384968&partnerID=8YFLogxK

U2 - 10.1007/s10955-012-0475-0

DO - 10.1007/s10955-012-0475-0

M3 - Article

AN - SCOPUS:84860384968

VL - 147

SP - 18

EP - 34

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -