Journal of Statistical Physics

, Volume 147, Issue 1, pp 18–34 | Cite as

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



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.


Gaussian field Membrane Pinning Confinement 



The author would like to thank the referee for his very useful comments. This work was partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B), No. 23740086.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyKeio UniversityYokohamaJapan

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