Abstract
We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.
References
C. A. Doty and D. S. Fisher,Phys. Rev. B 45:2167 (1992); S. Haas, J. Riera, and E. Dagotto,Phys. Rev. B 48:13174 (1994); K. J. Runge and G. T. Zimanyi,Phys. Rev. B 49:15212 (1994).
W. Wu, B. Ellmann, T. F. Rosenbaum, G. Aeppli, and D. H. Reich,Phys. Rev. Lett. 67:2076 (1991); W. Wu, D. Bitko, T. F. Rosenbaum, and G. Aeppli,Phys. Rev. Lett. 71:1919 (1993).
J. Miller and D. Huse,Phys. Rev. Lett. 70:3147 (1993); J. Ye, S. Sachdev, and N. Read,Phys. Rev. Lett. 70:4011 (1993).
Y. Y. Goldschmidt and P. Y. Lai,Phys. Rev. Lett. 64:2567 (1990), and references therein.
R. Oppermann,Nucl. Phys. B 401:507 (1993).
B. Boechat, R. R. dos Santos, and M. A. Continentino,Phys. Rev. B 49:6404 (1994); M. A. Continentino, B. Boechat, and R. R. dos Santos, preprint (1994).
H. Rieger and A. P. Young,Phys. Rev. Lett. 72: 4141 (1994).
M. Guo, R. N. Bhatt, and D. A. Huse,Phys. Rev. Lett. 72:4137 (1994).
D. S. Fisher,Phys. Rev. Lett. 69:534 (1992).
L. V. Mikheev and M. E. Fisher,Phys. Rev. B 49:378 (1994), and references therein.
B. M. McCoy and T. T. Wu,Phys. Rev. 176:631 (1968);188:982, 1014 (1969).
P. Hoever, W. F. Wolff, and J. Zittartz,Z. Phys. B 41:43 (1981).
R. Shankar and G. Murthy,Phys. Rev. B 36:536 (1987).
K. Binder and J. S. Wang,J. Stat. Phys. 55:87 (1989).
M. Suzuki,Prog. Theor. Phys. 56:1454 (1976).
L. Mikheev,Phys. Rev. B, submitted.
P. Kleban and G. Akinci,Phys. Rev. B 28:1466 (1983).
R. N. Bhatt and A. P. Young,Phys. Rev. B 37:5606 (1988).
A. Crisanti, G. Paladin, M. Serva, and A. Vulpiani,Phys. Rev. E 50:138 (1994).
B. Derrida and H. J. Hilhorst,J. Phys. C 14:L544 (1981).
A. Crisanti, S. Nicolis, G. Paladin, and A. Vulpiani,J. Phys. A 23:3083 (1990).
A. Crisanti, G. Paladin, and A. Vulpiani,Products of Random Matrices (Springer, Berlin, 1993).
A. Crisanti and H. Rieger, in preparation.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Crisanti, A., Rieger, H. Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis. J Stat Phys 77, 1087–1098 (1994). https://doi.org/10.1007/BF02183154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02183154