Abstract
We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and Möbius strip using Yang–Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang–Baxter techniques and functional equations can be used to study the conformal spectra of more general exactly solvable lattice models in these topologies. The results rely on certain properties of the eigenvalues which are confirmed numerically.
Similar content being viewed by others
REFERENCES
R. E. Behrend, P. A. Pearce, V. B. Petkova, and J.-B. Zuber, Phys. Lett. B 444:163–166 (1998); Nucl. Phys. B 579:707 (2000).
V. B. Petkova and J. B. Zuber, hep-th/0011021, Phys. Lett. B 504:57–164 (2001).
R. E. Behrend and P. A. Pearce, hep-th/0006094, J. Stat. Phys. 102:577 (2001).
G. Pradisi, A. Sagnotti, and Y. S. Stanev, hep-th/9503207, Phys. Lett. B 354:279–286 (1995); hep-th/9506014, Phys. Lett. B 356:230–238 (1995).
A. Sagnotti and Y. S. Stanev, Nucl. Phys. Proc. Suppl. B 55:200 (1997).
L. R. Huiszoon, A. N. Schellekens, and N. Sousa, hep-th/9909114, Phys. Lett. B 470: 95–102 (1999).
S. Yamaguchi, cond-mat/9704039, Prog. Theor. Phys. 97:703–707 (1997).
W. T. Lu and F. Y. Wu, Phys. Lett. A 259:108–114 (1999).
W. T. Lu and F. Y. Wu, cond-mat/0007325, Phys. Rev. E 63:026107 (2001).
W. T. Lu and F. Y. Wu, cond-mat/0110035, Phys. Lett. A 293:235–246 (2002).
K. Kaneda and Y. Okabe, Phys. Rev. Lett. 86:2134 (2001).
A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185:832 (1969).
V. Pasquier, Nucl. Phys. B 285:162 (1987); J. Phys. A 20:L1229, 5707 (1987).
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
A. Klümper and P. Pearce, J. Stat. Phys. 64:13 (1991); Phys. A 183:304 (1992).
D. O'Brien, P. A. Pearce, and S. O. Warnaar, Phys. A 228:63 (1996).
G. E. Andrews, R. J. Baxter, and P. J. Forrester, J. Stat. Phys. 35:193 (1984).
H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale, Phys. Rev. Lett. 56:742 (1986).
I. Affleck, Phys. Rev. Lett. 56:746 (1986).
E. Melzer, Int. J. Mod. Phys. A 9:1115 (1994).
R. E. Behrend, P. A. Pearce, and D. L. O'Brien, hep-th/9507118, J. Stat. Phys. (1996).
A. Berkovich, Nucl. Phys. B 431:315 (1994).
J. L. Cardy, Nucl. Phys. B 270:186 (1986); Nucl. Phys. B 275:200 (1986); Nucl. Phys. B 324:581 (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chui, C.H.O., Pearce, P.A. Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Möbius Strip. Journal of Statistical Physics 107, 1167–1205 (2002). https://doi.org/10.1023/A:1015113909363
Issue Date:
DOI: https://doi.org/10.1023/A:1015113909363