Abstract
The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects belowT c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.
Similar content being viewed by others
References
M. E. Fisher,Physica (Utrecht)A 106:28 (1981); L. P. Kadanoff and F. J. Wegner,Phys. Rev. B 4:3989 (1971); A. C. Brown,Phys. Rev. B 25:331 (1982); L. P. Kadanoff,Phys. Rev. B 24:5382 (1981).
R. Z. Bariev,Sov. Phys. JEPT 50:613 (1979);Theor. Math. Phys. 40:623 (1979);42:173 (1980).
M. E. Fisher and A. E. Ferdinand,Phys. Rev. Lett. 19:169 (1967).
B. M. McCoy and J. H. H. Perk,Phys. Rev. Lett. 44: 840 (1980); inThe Riemann Problem, Complete Integrability and Arithmetic Applications, D. Chudnovsky and G. Chudnovsky, eds.,Lecture Notes in Mathematics, Vol. 925 (Springer, Berlin, 1982), p. 12.
L. F. Ko, H. Au-Yang, and J. H. H. Perk,Phys. Rev. Lett. 54:1091 (1985); L. F. Ko, Ph. D. thesis, State University of New York, Stony Brook (1986).
T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch,Phys. Rev. B 13:316 (1976).
D. B. Abraham,Phys. Rev. Lett. 44:1165 (1980); inExact Results in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1986).
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,Nucl. Phys. B 240[FS]:514 (1984).
H. A. Kramers and G. H. Wannier,Phys. Rev. 60:252 (1941).
D. B. Abraham,J. Phys. A 14:L369 (1981).
B. Kaufman and L. Onsager,Phys. Rev. 76:1244 (1949); T. D. Shultz, D. C. Mattis, and E. H. Lieb,Rev. Mod. Phys. 36:856 (1964); B. M. McCoy and T. T. Wu,The Two-Dimensional hing Model (Harvard University Press, Cambridge, Massachusetts, 1973); D. B. Abraham,Commun. Math. Phys. 59:17,60:181 (1978).
B. M. McCoy, C. A. Tracy, and T. T. Wu,Phys. Rev. Lett. 38:793 (1977); inStatistical Mechanics and Statistical Methods in Theory and Application, U. Landman, ed. (Plenum Press, New York, 1977).
J. Palmer and C. Tracy,Adv. Appl. Math. 2:329 (1981).
W. J. Camp and M. E. Fisher,Phys. Rev. B 6:946 (1972); W. J. Camp,Phys. Rev. B 7:3187 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ko, LF. Spin-spin correlation function in the two-dimensional Ising model with linear defects. I.T<T c . J Stat Phys 52, 795–813 (1988). https://doi.org/10.1007/BF01019730
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01019730