Skip to main content
SpringerLink
Log in

Entropic Repulsion for Two Dimensional Multi-Layered Harmonic Crystals

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We consider two dimensional lattice free fields (harmonic crystals) and study the asymptotic behavior of the fields under the constraint that each field lies above a hard-wall and is forced to be piled on top of another. This problem is the so-called entropic repulsion and our result extends that of ref. 2 which studied the higher dimensional case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. D. Bertacchi and G. Giacomin, Enhanced interface repulsion from quenched hard-wall randomness, Probab. Theory Rel. 124:487–516 (2002).

    Google Scholar 

  2. D. Bertacchi and G. Giacomin, Wall Repulsion and Mutual Interface Repulsion: An Harmonic Crystal Model in High Dimensions, preprint (2002).

  3. E. Bolthausen, J.-D. Deuschel, and G. Giacomin, Entropic repulsion and the maximum of two dimensional harmonic crystal, Ann. Prob. 29:1670–1692 (2001).

    Google Scholar 

  4. E. Bolthausen, J.-D. Deuschel, and O. Zeitouni, Entropic repulsion of the lattice free field, Comm. Math. Phys. 170:417–443 (1995).

    Google Scholar 

  5. J. Bricmont, Random surfaces in statistical mechanics in Wetting phenomena, in Proceedings of the Second Workshop held at the University of Mons, October 17–19, 1988, J. De Coninck and F. Dunlop, eds., Lecture Notes in Physics, Vol. 354 (Springer-Verlag, Berlin).

    Google Scholar 

  6. J. Bricmont, A. El Mellouki, and J. Fröhlich, Random surfaces in Statistical Mechanics —roughening, rounding, wetting, J. Stat. Phys. 42:743–798 (1986).

    Google Scholar 

  7. J.-D. Deuschel, Entropic repulsion of the lattice free field. II. The 0-boundary case, Comm. Math. Phys. 181:647–665 (1996).

    Google Scholar 

  8. J.-D. Deuschel and G. Giacomin, Entropic repulsion for the free field: pathwise characterization in d ≥ 3, Comm. Math. Phys. 206:447–462 (1999).

    Google Scholar 

  9. J.-D. Deuschel and G. Giacomin, Entropic repulsion for massless fields, Stoch. Proc. Appl. 89:333–354 (2000).

    Google Scholar 

  10. G. Giacomin, Anharmonic lattices, random walks, and random interfaces, Transworld Research Network, Statistical Physics 1:97–118 (2000).

    Google Scholar 

  11. G. Giacomin, Aspects of Statistical Mechanics of Random Surfaces, notes of the lectures given at IHP in the fall 2001, preprint.

  12. G. F. Lawler, Intersections of Random Walks (Birkhaüser, 1991).

  13. R. Lipowsky, From bunches of membranes to bundle of strings, Z. Phys. B 97:193–203 (1995).

    Google Scholar 

  14. H. Sakagawa, Entropic repulsion for a Gaussian lattice field with certain finite range interaction, J. Math. Phys. 44:2939–2951 (2003).

    Google Scholar 

  15. A. Volmer, U. Seifert, and R. Lipowsky, Critical behavior of interacting surfaces with tension, Eur. Phys. J. B 5:811–823 (1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama, 223-8522, Japan

    Hironobu Sakagawa

Authors
  1. Hironobu Sakagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sakagawa, H. Entropic Repulsion for Two Dimensional Multi-Layered Harmonic Crystals. Journal of Statistical Physics 114, 37–49 (2004). https://doi.org/10.1023/B:JOSS.0000003103.86191.24

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOSS.0000003103.86191.24

Search

Navigation