Abstract
We extend the well-known Mattis model to the case of asymmetric bond distributions. Although the partition function is identical with that of the pure ferromagnetic Ising model (FIM) when the external field is absent, the response to the external field is nontrivial even at zero field. There are some exact relations between the present model and the FIM in the correlation functions, from which the phase diagram and critical exponents can be determined. Multicritical behavior and some other interesting phenomena typical for a random system are demonstrated by this model.
Similar content being viewed by others
References
K. Binder and A. P. Young,Rev. Mod. Phys. 58:924 (1986).
D. Chowdury,Spin Glass and Other Frustrated Systems (Princeton University Press, Princeton, New Jersey, 1986).
M. Mezard, G. Parisi, and A. Virasoro,Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
I. Morgenstern and K. Binder,Phys. Rev. Lett. 43:1615 (1979);Phys. Rev. B 22:288 (1980).
H. Nishimori,Prog. Theor. Phys. 66:1169 (1981).
R. N. Bhatt and A. P. Young,Phys. Rev. Lett. 54:924 (1985).
A. T. Ogielski and I. Morgenstern,Phys. Rev. Lett. 54:928 (1985).
A. T. Ogielski,Phys. Rev. B 32:7384 (1985).
R. R. P. Singh and S. Chakravarty,Phys. Rev. Lett. 57:245 (1986);Phys. Rev. B 36:546, 559 (1987).
Y. Ozeki and H. Nishimori,J. Phys. Soc. Jpn. 56:1568, 3265 (1987).
Y. Ozeki,J. Phys. Soc. Jpn. 59:3531 (1990).
Y. Ueno and Y. Ozeki,J. Stat. Phys. 64:227 (1991).
D. C. Mattis,Phys. Lett. 56A:421 (1976);60A:492 (1977).
D. Ruelle,Statistical Mechanics: Rigorous Results (Addison-Wesley, Redwood City, California, 1969).
B. M. McCoy and T. T. Wu,The Two-Dimensional Ising Model (Harvard University Press, Cambridge, Massachusetts, 1973).
Y. Imry and S. K. Ma,Phys. Rev. Lett. 35:1399 (1975).
J. Imbrie,Commun. Math. Phys. 98:145 (1985).
J. Bricmont and A. Kupiainen,Phys. Rev. Lett. 59:1829 (1987);Commun. Math. Phys. 116:539 (1988).
J. Wehr and M. Aizenman,Phys. Rev. Lett. 62A:2503 (1989);Commun. Math. Phys. 130:489 (1990);J. Stat. Phys. 60:287 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ozeki, Y. Phase diagram and critical properties of the asymmetric Mattis model. J Stat Phys 71, 759–773 (1993). https://doi.org/10.1007/BF01058446
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058446