Abstract
Partition functions of critical 2D models on a torus can be derived from their microscopic formulation and their free field representation in the continuum limit. This is worked out explicitly for theO(n) andQ-state Potts model. Forn orQ integer we recover results obtained from conformal invariance, but our procedure also extends to nonintegral values. In the latter case the expansion on characters of the Virasoro algebra involves real coefficients of either sign. The operator content of both models is discussed in detail.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,Nucl. Phys. B 241:333 (1984).
J. L. Cardy, inPhase Transitions and Critical Phenomena, Vol.11, C. Domb and J. Lebowitz, eds. (Academic Press, 1986).
L. P. Kadanoff,J. Phys. A 11:1399 (1978); A. Luther, I. Peschel,Phys. Rev. B 12:3908 (1975); H. J. F. Knops,Ann. Phys. 128:448 (1981).
B. Nienhuis,J. Stat. Phys. 34:731 (1984); M. P. M. den Nijs,Phy. Rev. B 27:1674 (1983);J. Phys. A 17:L295 (1984).
V. S. Dotensko and V. A. Fateev,Nucl. Phys. B 240:312 (1984);251:691 (1985).
B. Nienhuis and H. J. F. Knops,Phys. Rev. B 32:1872 (1985).
J. L. Cardy,Nucl. Phys. B 270:186 (1986).
C. Itzykson and J. B. Zuber,Nucl. Phys. B 275:580 (1986).
D. Gepner,Nucl. Phys. B 287:111 (1987).
A. Cappelli, C. Itzykson, and J. B. Zuber,Nucl. Phys. B 280:445 (1987).
P. Di Francesco, H. Saleur, and J. B. Zuber,Nucl. Phys. B 285:454 (1987).
S. K. Yang,Nucl. Phys. B 285:183 (1987).
H. Blöte, J. L. Cardy, and M. P. Nightingale,Phys. Rev. Lett. 56:742 (1986).
I. Affleck,Phys. Rev. Lett. 56:746 (1986).
J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:118 (1973); J. M. Kosterlitz,J. Phys. C 7:1046 (1971); D. J. Amit, Y. Y. Goldschmidt, and G. Grinstein,J. Phys. A 13:585 (1980).
J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. P. Nelson,Phys. Rev. B 16:12 (1977).
D. J. Gross, J. A. Harvey, E. Martinec, and R. Hohm,Nucl. Phys. B 256:253 (1985).
R. J. Baxter, inExactly Solved Models in Statistical Physics (Academic Press, 1982).
D. Gepner and Z. Qiu,Nucl. Phys. B 285:423 (1987).
H. Saleur,J. Phys. A 20:455 (1987).
H. Saleur,Phys. Rev. B 35:3657 (1987).
G. Parisi and N. Sourlas,J. Phys. Lett. (Paris) 41:L403 (1980).
B. Duplantier and H. Saleur, inNucl. Phys. B, to appear.
P. G.de Gennes,Phys. Lett. 38A:339 (1972).
R. J. Baxter, S. B. Kelland, and F. Y. Wu,J. Phys. A 9:397 (1976).
H. Saleur and B. Duplantier,Phys. Rev. Lett. 2325 (1987).
B. Nienhuis,J. Phys. A 15:199 (1982).
V. Pasquier, Saclay preprints SPhT/87-014;Nucl. Phys. B 285:162 (1987);J. Phys. A. 20:L221 (1987);J. Phys. A 0:L217 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
di Francesco, P., Saleur, H. & Zuber, J.B. Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models. J Stat Phys 49, 57–79 (1987). https://doi.org/10.1007/BF01009954
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01009954