J. Phys. Soc. Jpn. 55 (1986) pp. 2605-2617  |Next Article|  |Table of Contents|
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Exactly Solvable IRF Models. V. A Further New Hierarchy

Atsuo Kuniba, Yasuhiro Akutsu and Miki Wadati

(Received March 14, 1986)

It is shown that a k-state IRF model (σ=0, 1, ···, k-1), with a condition k-2≦σ_i+σ_j≦k on adjacent spins σ_i and σ_j, is exactly solvable for all k(k≧3). This proves the existence of a new hierarchy of solvable IRF models. It is also shown that the k-state IRF model is equivalent to a 3k-state solid on solid (SOS) model. Considering all the known results, it is predicted that for an arbitrary set of integers L and f(L≦0, f≦1) there exists a solvable IRF model with the hard core condition L≧σ_i+σ_j≦L+f. ©1986 The Physical Society of Japan

URL: http://jpsj.ipap.jp/link?JPSJ/55/2605/
DOI: 10.1143/JPSJ.55.2605

References | Citing Articles (12)

1. G. E. Andrews, R. J. Baxter and P. J. Forrester: J. Stat. Phys. 35 (1984) 193; P. J. Forrester and R. J. Baxter: J. Stat. Phys. 38 (1985) 435.
2. Y. Akutsu, A. Kuniba and M. Wadati: J. Phys. Soc. Jpn. 55 (1986) 1466[IPAP].
3. Y. Akutsu, A. Kuniba and M. Wadati: J. Phys. Soc. Jpn. 55 (1986) 1880[IPAP].
4. M. Jimbo and T. Miwa: Physica 15D (1985) 336[Elsevier].
5. R. J. Baxter: J. Phys. A13 (1980) L61[IoP STACKS].
6. R. J. Baxter: Exactly Solved Models in Statistical Mechanics (Academic, Press, London, 1982).
7. L. D. Faddeev: Sov. Sci. Rev. Math. Phys. C1 (1981) 107; H. B. Thacker: Rev. Mod. Phys. 53 (1981) 253[APS]; P. P. Kulish and E. K. Sklyanin: Lecture Notes in Physics Vol. 151 (Springer, 1982) p. 61; M. Wadati: Quantum Inverse Scattering Method, in Dynamical Problems in Soliton Systems, ed. S. Takeno (Springer-Verlag, 1985) p. 68.
8. R. J. Baxter: J. Stat. Phys. 26 (1981) 427.
9. G. E. Andrews: The Theory of Partitions (Addition-Wesley, 1976).
10. B. Gordon: Am. J. Math. 83 (1961) 393.
11. A. Kuniba, Y. Akutsu and M. Wadati: J. Phys. Soc. Jpn. 55 (1986) 1092[IPAP].
12. R. J. Baxter and G. E. Andrews: preprint.
13. A. Kuniba, Y. Akutsu and M. Wadati: J. Phys. Soc. Jpn. 55 (1986) 2166[IPAP].
14. A. A. Belavin, A. B. Zamolodchikov and A. M. Polyakov: J. Stat. Phys. 34 (1984) 763; D. Friedan, Z. Qiu and S. Shenker: Phys. Rev. Lett. 52 (1984) 1575[APS].
15. D. A. Huse: Phys. Rev. B30 (1984) 3908[APS].
16. J. Lepowsky and R. L. Wilson: Proc. Nat. Acad. Sci. U.S.A. 78 (1981) 7254.
17. V. G. Kac: Infinite Dimensional Lie Algebras (Birkhäuser, Boston, 1983).