Abstract
The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional,φ 4, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well φ4 model, the border model, and the double-wellφ 4 model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.
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,Nucl. Phys. B 240[FS12]:514 (1984).
D. Friedan, Z. Qiu, and S. Shenker,Phys. Rev. Lett. 52:1575 (1984).
J. L. Cardy,J. Phys. A 17:L385 (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).
A. B. Zamolodchikov,JEPT Lett. 43:730 (1986).
J. L. Cardy,Phys. Rev. Lett. 60:2709 (1988).
R. R. P. Singh and G. A. Baker, Jr.,Phys. Rev. Lett. 66:1 (1991); G. A. Baker, Jr., and R. R. P. Singh,Physica A 177:123 (1991).
J. L. Cardy, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987), p. 55.
G. A. Baker, Jr.,J. Math. Phys. 24:143 (1983);J. Phys. A 17:L621 (1984); G. A. Baker, Jr., and J. D. Johnson,J. Phys. A 17:L275 (1984).
M. Barma and M. E. Fisher,Phys. Rev. Lett. 53:1935 (1984);Phys. Rev. B 31:5954 (1985).
G. A. Baker, Jr.,Phys. Rev. Lett. 60:1844 (1988).
A. Milchev, D. W. Heermann, and K. Binder,J. Stat. Phys. 44:749 (1986).
R. Toral and A. Chakrabari,Phys. Rev. B 42:2445 (1990).
A. D. Brace,J. Phys. A 18:L873 (1985).
G. A. Baker, Jr., and J. M. Kincaid,J. Stat. Phys. 24:469 (1981).
Xidi Wang, D. K. Campbell, and J. E. Gubernatis, Symmetry breaking in a quantum double-well chain: Application to hydrogen bonded materials, in preparation.
S. Duane,Nucl. Phys. B 257:652 (1985); S. Duane and J. B. Kogut,Nucl. Phys. B 275:398 (1986); S. Duane, A. D. Kennedy, B. J. Pendelton, and D. Roweth,Phys. Lett. B 195:216 (1987).
A. E. Ferdinand, Thesis, Cornell University, Ithaca, New York (1967).
G. A. Baker, Jr., and J. D. Johnson,J. Phys. A 17:L275 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, X., Baker, G.A. Monte carlo calculations of the conformal charge. J Stat Phys 69, 1069–1095 (1992). https://doi.org/10.1007/BF01058762
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058762