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Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities

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Abstract

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each sitei of the lattice there is associated an integer heightl i restricted to the range 1⩽l i r−1. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a parameterη. In an earlier paper we considered the caseη=K/r. Here we generalize those considerations to the caseη=sK/r, s an integer relatively prime tor. We are again led to generalizations of the Rogers-Ramanujan identities.

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References

  1. G. E. Andrews, R. J. Baxter, and P. J. Forrester,J. Stat. Phys. 35:193 (1984).

    Google Scholar 

  2. R. J. Baxter,J. Phys. A 13:L61 (1980).

    Google Scholar 

  3. D. A. Huse, Bell Laboratories preprint.

  4. I. Schur,Sitzungsber. Akad. Wissensch., Berlin, Phys. Math. K1., 488 (1926).

  5. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).

    Google Scholar 

  6. R. J. Baxter,J. Stat. Phys. 28:1 (1982).

    Google Scholar 

  7. G. E. Andrews,The Theory of Partitions (Addison-Wesley, Reading, Massachusetts, 1976).

    Google Scholar 

  8. E. T. Whittaker and G. N. Watson,A Course of Modern Analysis (Cambridge University Press, London, 1950).

    Google Scholar 

  9. B. Gordon,Am. J. Math. 83:393 (1961).

    Google Scholar 

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Forrester, P.J., Baxter, R.J. Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities. J Stat Phys 38, 435–472 (1985). https://doi.org/10.1007/BF01010471

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  • DOI: https://doi.org/10.1007/BF01010471

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