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Lattice systems with a continuous symmetry

III. Low temperature asymptotic expansion for the plane rotator model

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Abstract

We prove that the expansion in powers of the temperatureT of the correlation functions and the free energy of the plane rotator model on ad-dimensional lattice is asymptotic to all orders inT. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures ford=3.

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References

  1. Bricmont, J., Fontaine, J.R.: Correlation inequalities and contour estimates (in preparation)

  2. Bricmont, J., Fontaine, J.R., Landau, L.J.: Commun. Math. Phys.56, 281 (1977)

    Article  Google Scholar 

  3. Bricmont, J., Fontaine, J.R., Lebowitz, J.L., Spencer, T.: Lattice systems with a continuous symmetry. I. Commun. Math. Phys.78, 281–302 (1980)

    Article  Google Scholar 

  4. Bricmont, J., Fontaine, J.R., Lebowitz, J.L., Spencer, T.: Lattice systems with a continuous symmetry. II. Commun. Math. Phys.78, 363–371 (1981)

    Article  Google Scholar 

  5. Brascamp, H.J., Lieb, E.H.: J. Funct. Anal.22, 366 (1976)

    Article  Google Scholar 

  6. Brezin, E.: Proceedings of the 13th IUPAP Conference on Statistical Physics [(ed.) Cabib, D., Kuper, C., and Reiss]. Haifa 1977

  7. Dobrushin, R.L.: Funct. Anal. and Appl.2, 292 (1968)

    Article  Google Scholar 

  8. Dobrushin, R.L., Shlosman, S.B.: Commun. Math. Phys.42, 31 (1975)

    Article  Google Scholar 

  9. Dunlop, F., Newman, C.: Commun. Math. Phys.44, 223 (1975)

    Article  Google Scholar 

  10. Dunlop, F.: Commun. Math. Phys.49, 247 (1976)

    Article  Google Scholar 

  11. Elitzur, S.: The applicability of perturbation expansion to two-dimensional Goldstone systems. I.A.S. Princeton preprint 1019

  12. Fröhlich, J., Guerra, F., Robinson, D., Stora, R. (eds.): Marseille Conference C.N.R.S. 1975

  13. Fröhlich, J., Simon, B., Spencer, T.: Commun. Math. Phys.50, 79 (1976)

    Article  Google Scholar 

  14. Ginibre, J.: Commun. Math. Phys.16, 310 (1970)

    Article  Google Scholar 

  15. Hegerfeldt, G.: Commun. Math. Phys.57, 259 (1977)

    Article  Google Scholar 

  16. Kunz, H., Pfister, C.E., Vuillermot, J.: Phys. A. Math. Gen.9, 1673 (1976)

    Article  Google Scholar 

  17. Lanford, O., Ruelle, D.: Commun. Math. Phys.13, 194 (1969)

    Article  Google Scholar 

  18. Lebowitz, J., Penrose, O.: Commun. Math. Phys.11, 99 (1968)

    Article  Google Scholar 

  19. Lebowitz, J., Penrose, O.: Phys. Rev. Lett.35, 549 (1975)

    Article  Google Scholar 

  20. Lee, T.D., Yang, C.N.: Phys. Rev.87, 410 (1952)

    Article  Google Scholar 

  21. Mermin, D.: J. Math. Phys.6, 1061 (1967)

    Article  Google Scholar 

  22. Messager, A., Miracle-Sole, S.: J. Stat. Phys.17, 245 (1977)

    Article  Google Scholar 

  23. Messager, A., Miracle-Sole, S., Pfister, C.E.: Commun. Math. Phys.58, 19 (1978)

    Article  Google Scholar 

  24. Schrader, R.: Phys. Rev. B15, 2798 (1977)

    Article  Google Scholar 

  25. Sokal, A.: In preparation

Download references

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08540, Princeton, NJ, USA

    Jean Bricmont

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Jean-Raymond Fontaine, Joel L. Lebowitz & Thomas Spencer

  3. Department of Mathematics and Physics, Princeton University, 08540, Princeton, NJ, USA

    Elliott H. Lieb

Authors
  1. Jean Bricmont
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  2. Jean-Raymond Fontaine
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  3. Joel L. Lebowitz
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  4. Elliott H. Lieb
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  5. Thomas Spencer
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Additional information

Communicated by A. Jaffe

Supported by NSF Grant No. MCS 78-01885

Supported by NSF Grant No. PHY 78-15920

Supported by NSF Grant No. DMR 73-04355

Supported by NSF Grant No. PHY-7825390 A01

On leave from: Institut de Physique Théorique, Université de Louvain, Belgium

Also: Department of Physics

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Bricmont, J., Fontaine, JR., Lebowitz, J.L. et al. Lattice systems with a continuous symmetry. Commun.Math. Phys. 78, 545–566 (1981). https://doi.org/10.1007/BF02046764

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  • DOI: https://doi.org/10.1007/BF02046764

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