Abstract
The local state probabilities (LSPs) are exactly computed for four hierarchies of solvable lattice models. They are restricted solid-on-solid (RSOS) models whose local states and their adjacent conditions are specified by Dinkin diagrams of typesA n,D n,D (1) n andA (1) n . The LSPs are expressed in terms of modular functions characterized by branching identities among the theta functions. Their automorphic properties are used to study the critical behaviors. Some fine structures are found in the spectrum of the critical exponents.
Similar content being viewed by others
References
R. J. Baxter,J. Stat. Phys. 26:427 (1981).
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
G. E. Andrews, R. J. Baxter, and P. J. Forrester,J. Stat. Phys. 35:193 (1984).
D. A. Huse,Phys. Rev. B 30:3908 (1984).
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,Nucl. Phys. B 241:333 (1984).
E. Date, M. Jimbo, T. Miwa, and M. Okado,Lett. Math. Phys. 12:209 (1986).
E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado,Nucl. Phys. B 290[FS20]:231 (1987).
E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado,Adv. Studies Pure Math. 16:17 (1988).
A. Kuniba and T. Yajima,J. Phys. A: Math. Gen. 21:519 (1988).
M. Jimbo, T. Miwa, and M. Okado,Lett. Math. Phys. 14:123 (1987).
V. Pasquier,J. Phys. A: Math. Gen. 20:L217, L221 (1987).
Y. Akutsu, A. Kuniba, and M. Wadati,J. Phys. Soc. Jpn. 55:1880 (1986).
V. Pasquier,Nucl. Phys. B 285[FS19]:162 (1987).
M. Jimbo, T. Miwa, and M. Okado,Commun. Math. Phys. 116:507 (1988).
B. L. Feigin and D. B. Fuchs,Fund. Anal. Appl. 17:91 (1987);Lect. Notes Math. 1060:230 (1984); A. Rocha-Caridi, inVertex Operators in Mathematical Physics, J. Lepowsky, S. Mandelstam, and I. M. Singer, eds. (Springer, New York, 1985).
H. N. V. Temperley and E. H. Lieb,Proc. Roy. Soc. Lond. A 322:251 (1971).
R. J. Baxter,J. Stat. Phys. 28:1 (1982).
A. Kuniba, Y. Akutsu, and M. Wadati,J. Phys. Soc. Jpn. 55:3285 (1986).
V. G. Kac,Infinite Dimensional Lie Algebras (Birkhäuser, Boston, 1984).
M. Jimbo and T. Miwa,Physica 15D:335 (1985).
G. E. Andrews,The Theory of Partitions (Addison-Wesley, Reading, Massachusetts, 1976).
P. Goddard, A. Kent, and D. Olive,Phys. Lett. B 152:88 (1985).
V. A. Fateev and A. B. Zamolodchikov,Sov. Phys. JETP 62:215 (1985).
M. A. Bershadsky, V. G. Knizhnik, and M. G. Teitelman,Phys. Lett. B 151:31 (1985); D. Friedan, Z. Qiu, and S. Shenker,Phys. Lett. B 37 (1985).
J. L. Cardy,Nucl. Phys. B 270[FS160]:186 (1986).
A. Cappelli, C. Itzykson, and J.-B. Zuber,Nucl. Phys. B 280[FS18]:445 (1987); D. Gepner and Z. Qiu,Nucl. Phys. B 285[FS19]:423 (1987); A. Kato,Mod. Phys. Lett. A 2:585 (1987).
V. F. R. Jones,Invent. Math. 72:1 (1983).
H. Wenzl, Ph. D. Thesis, University of Pennsylvania (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuniba, A., Yajima, T. Local state probabilities for solvable restricted solid-on-solid models:A n,D n,D (1) n , andA (1) n . J Stat Phys 52, 829–883 (1988). https://doi.org/10.1007/BF01019732
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01019732