Abstract
We introduce and study the critical properties of the tripletXY quantum chain. This system is described in terms of three-spin interactions and is the generalization of the standardXY quantum chain. We show that this model, with periodic boundaries, has a local gauge invariance and can be described by the composition of two triplet Ising models, with general toroidal boundary conditions. From this composition the phase diagram as well the conformai anomaly and critical exponents are determined by exploring their relations with the mass gap amplitudes predicted by conformai invariance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. J. Baxter,Ann. Phys. (N.Y.)70:193–228 (1972).
J. Ashkin and E. Teller,Phys. Rev. 64:178–184 (1943).
F. C. Alcaraz and M. N. Barber,J. Stat. Phys. 46:435–453 (1987).
J. M. Debierre and L. Turban,J. Phys. A: Math. Gen. 16:3571–3584 (1983).
A. M. Polyakov,Sov. Phys. JETP Lett. 12:381 (1970).
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,J. Stat. Phys. 34:763 (1984);Nucl. Phys. B 241:333 (1984).
J. L. Cardy, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1987).
J. L. Cardy,J. Phys. A: Math. Gen. 17:L385–357 (1984).
J. L. Cardy,Nucl. Phys. B 270[FS16]:186 (1986).
M. N. Barber,Phys. Rep. 59:375–409 (1980).
G. v. Gehlen, V. Rittenberg, and H. J. Ruegg,J. Phys. A: Math. Gen. 19:107–119 (1986).
L. Kadanoff and A. C. Brown,Ann. Phys. (N.Y.)121:318 (1979).
J. M. van den Broeck and L. W. Schwartz,SIAM J. Math. Anal. 10:658 (1979).
C. J. Hamer and M. N. Barber,J. Phys. A: Math. Gen. 14:2009–2025 (1981).
M. Henkel, inFinite-Size Scaling and Numerical Simulations of Statistical Systems, V. Privman, ed. (World Scientific, Singapore, in press).
J. L. Cardy,J. Phys. A: Math. Gen. 19:L1093 (1986).
F. C. Alcaraz, M. N. Barber, and M. T. Batchelor,Ann. Phys. (N.Y.)182:280–343 (1988).
K. Binder, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1983).
G. v. Gehlen and V. Rittenberg,J. Phys. A: Math. Gen. 19:L1039 (1986).
F. C. Alcaraz, M. N. Barber, M. T. Batchelor, R. J. Baxter, and G. R. W. Quispel,J. Phys. A: Math. Gen. 20:6397–6409 (1987).
M. Baake, G. v. Gehlen, and V. Rittenberg,J. Phys. A: Math. Gen. 20:L479, L487 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alcaraz, F.C., Constantinidis, C.P. Conformal invariance and the critical behavior of the tripletXY quantum chain. J Stat Phys 60, 639–657 (1990). https://doi.org/10.1007/BF01025986
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01025986