Journal of Statistical Physics

, Volume 102, Issue 3–4, pp 1019–1027 | Cite as

The Inversion Relation and the Dilute A3, 4, 6 Eigenspectrum

  • Katherine A. Seaton
  • Murray T. Batchelor


On the basis of the result obtained by applying Baxter's exact perturbative approach to the dilute A3 model to give the E8 mass spectrum, the dilute AL inversion relation was used to predict the eigenspectra in the L=4 and L=6 cases (corresponding to E7 and E6 respectively). In calculating the next-to-leading term in the correlation lengths, or equivalently masses, the inversion relation condition gives a surprisingly simple result in all three cases, and for all masses.

Ising model in a field dilute A model integrable quantum field theory mass spectrum 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. B. Zamolodchikov, Adv. Stud. Pure Math. 19:641–674 (1989); Int. J. Mod. Phys. A 4:4235–4248 (1989).Google Scholar
  2. 2.
    S. O. Warnaar, B. Nienhuis, and K. A. Seaton, Phys. Rev. Lett. 69:710–712 (1992); Int. J. Mod. Phys. B 7:3727–3736 (1993).Google Scholar
  3. 3.
    R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).Google Scholar
  4. 4.
    S. O. Warnaar, P. A. Pearce, K. A. Seaton, and B. Nienhuis, J. Stat. Phys. 74:469–531 (1994).Google Scholar
  5. 5.
    M. T. Batchelor, V. Fridkin, and Y. K. Zhou, J. Phys. A 29:L61–67 (1996).Google Scholar
  6. 6.
    S. O. Warnaar and P. A. Pearce, J. Phys. A: Math. Gen. 27:L891–L897 (1994); Int. Journ. Mod. Phys. A 11:291–311 (1996).Google Scholar
  7. 7.
    V. V. Bazhanov, B. Nienhuis, and S. O. Warnaar, Phys. Lett. B 322:198–206 (1994).Google Scholar
  8. 8.
    U. Grimm and B. Nienhuis, Phys. Rev. E 55:5011–5025 (1997).Google Scholar
  9. 9.
    B. M. McCoy and W. P. Orrick, Phys. Lett. A 230:24–32 (1997).Google Scholar
  10. 10.
    M. T. Batchelor and K. A. Seaton, J. Phys. A 30:L479–484 (1997).Google Scholar
  11. 11.
    M. T. Batchelor and K. A. Seaton, Nucl. Phys. B 520:697–744 (1998).Google Scholar
  12. 12.
    J. Suzuki, Nucl. Phys. B 528:683–700 (1998).Google Scholar
  13. 13.
    Y. Hara, M. Jimbo, H. Konno, S. Odake, and J. Shiraishi, J. Math. Phys. 40:3791–3826 (1999).Google Scholar
  14. 14.
    V. A. Fateev and A. B. Zamolodchikov, Int. Journ. Mod. Phys. A 5:1025–1048 (1990).Google Scholar
  15. 15.
    M. T. Batchelor and K. A. Seaton, Eur. Phys. J. B 5:719–725 (1998); K. A. Seaton and M. T. Batchelor, Group22: Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, S. P. Corney, R. Delbourgo, and P. D. Jarvis, eds. (International Press, Cambridge, MA, 1999), pp. 274–278.Google Scholar
  16. 16.
    J. Suzuki, in Physical Combinatorics, M. Kashiwara and T. Miwa, eds. (Birkhäuser Boston, Cambridge, MA, 2000), pp. 217–247.Google Scholar
  17. 17.
    M. Caselle and M. Hasenbusch, Nucl. Phys. B 579:667–703 (2000).Google Scholar
  18. 18.
    R. J. Baxter, Ann. Phys. (N. Y.) 70:193–228 (1972).Google Scholar
  19. 19.
    P. A. Pearce and M. T. Batchelor, J. Stat. Phys. 60:77–135 (1990).Google Scholar
  20. 20.
    B. Kostant, Proc. Natl. Acad. Sci. USA 81:5275–5277 (1984).Google Scholar
  21. 21.
    H. W. Braden, E. Corrigan, P. E. Dorey, and R. Sasaki, Nucl. Phys. B 338:689–746 (1990).Google Scholar
  22. 22.
    V. A. Fateev, Phys. Lett. B 324:45–51 (1994).Google Scholar
  23. 23.
    G. Delfino and G. Mussardo, Nucl. Phys. B 455:724–758 (1995).Google Scholar
  24. 24.
    T. J. Hollowood and P. Mansfield, Phys. Lett. B 226:73–79 (1989).Google Scholar
  25. 25.
    U. Grimm and B. Nienhuis, private communication.Google Scholar
  26. 26.
    K. A. Seaton and M. T. Batchelor, in preparation.Google Scholar
  27. 27.
    A. Erdélyi et al., Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Katherine A. Seaton
    • 1
  • Murray T. Batchelor
    • 2
  1. 1.School of Mathematical and Statistical SciencesLa Trobe UniversityBundooraAustralia
  2. 2.Department of MathematicsAustralian National UniversityCanberraAustralia

Personalised recommendations