Abstract
The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J v, while all the horizontal couplings take the same positive value J h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 32:1792 (1975).
M. Mezard, G. Parisi, and M. Virasoro, Spin glass theory and beyond (World Scientific Singapore, 1988).
M. E. Fisher and W. Selke, Phys. Rev. Lett. 44:1502 (1980).
F. Koukiou, Europhys. Lett. 7:297 (1992).
L. Saul and M. Kardar, Phys. Rev. E 48:48 (1993).
J. L. Van Hemmen and R. G. Palmer, J. Phys. A: Math. Gen. 15:3881 (1982).
H.-F. Cheung and W. McMillan, J. Phys. C 11:7027 (1983).
G. Paladin, M. Pasquini, and M. Serva, Int. J. Mod. Phys. B 9:399 (1995).
G. Paladin, M. Pasquini, and M. Serva, J. Phys. I (France) 5:337 (1995).
S. Scarlatti, M. Serva, and M. Pasquini, J. Stat. Phys. 80:337 (1995).
M. Serva, G. Paladin, and J. Raboanary, Phys. Rev. E 52:R9 (1996).
G. Paladin and M. Serva, J. Phys. A: Math. Gen. 29:1381 (1996).
G. Paladin and M. Serva, Phys. Rev. E 54:4637 (1996).
M. Pasquini and M. Serva, Phys. Rev. E 56:2751 (1997).
M. Serva, Phys. Rev. Rapid Communications 56:R2339 (1997).
R. Shankar and Ganpathy Murthy, Phys. Rev. B 36:536 (1987).
B. Derrida, J. Vannimenus, and Y. Pomeau, J. Phys. C11:4749 (1978).
B. Derrida and H. J. Hilorst, J. Phys. CA16:2641 (1983).
J. Deutsch and G. Paladin, Phys. Rev. Lett. 62:695 (1988).
G. Paladin and M. Serva, Phys. Rev. Lett. 69:706 (1992).
A. Crisanti, G. Paladin, M. Serva, and A. Vulpiani, Phys. Rev. Lett. 71:789 (1993).
A. Crisanti, G. Paladin, M. Serva, and A. Vulpiani, J. Phys I (France) 3:1993 (1993).
A. Crisanti, G. Paladin, M. Serva, and A. Vulpiani, Phys. Rev. E 49:R953 (1994).
M. Pasquini, G. Paladin, and M. Serva, Phys. Rev. E 51:2006 (1995).
M. Pasquini, G. Paladin, and M. Serva, J. Stat. Phys. 80:357 (1995).
G. Grinstein and D. Mukamel, Phys. Rev. B 27:4503 (1983).
T. D. Schultz, D. C. Mattis, and E. H. Lieb, Rev. Mod. Phys. 36:856 (1964).
B. M. McCoy and T. T. Wu, Phys. Rev. 76:631 (1968).
B. M. McCoy, Phys. Rev. B 2:2795 (1970).
B. Derrida and Y. Shnidman, J. Phys. Lett. (France) 45:L–507 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Serva, M. 2D Ising Model with Layers of Quenched Spins. Journal of Statistical Physics 91, 31–45 (1998). https://doi.org/10.1023/A:1023079702378
Issue Date:
DOI: https://doi.org/10.1023/A:1023079702378