Abstract
We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Hubbard,Proc. Roy. Soc. London A 276:283 (1963);281:401 (1964).
T. Moriya, ed., Electron Correlation and Magnetism in Narrow-Band Systems, (Springer, New York, 1981).
E. Lieb and F. Wu,Phys. Rev. Lett. 20:1445 (1968).
J. E. Hirsch, D. J. Scalapino, R. L. Sugar, and R. Blankenbecler,Phys. Rev. B 26:5033 (1982).
J. E. Hirsch,Phys. Rev. B 28:4059 (1983).
J. E. Hirsch, to be published.
J. E. Hirsch,Phys. Rev. Lett. 53:2327 (1984).
J. E. Hirsch,Phys. Rev. B 31:4403 (1985).
R. Blankenbecler, D. J. Scalapino, and R. L. Sugar,Phys. Rev. D 24:2278 (1981); D. J. Scalapino and R. L. Sugar,Phys. Rev. B 24:4295 (1981);Phys. Rev. Lett. 46:519 (1981).
J. E. Hirsch (unpublished).
F. T. Dyson,Phys. Rev. 92:1331 (1953).
See also, D. Ceperley, G. V. Chester, and M. W. Kalos,Phys. Rev. B 16:3081 (1977).
K. Binder,Phys. Lett. A 30:273 (1969); H. Müller-Krumbhaar and K. Binder,Z. Physik 254:269 (1972).
J. E. Hirsch (unpublished).
F. Y. Wu,Rev. Mod. Phys. 54:235 (1982).
G. S. Rushbrooke, G. A. Baker, Jr., and P. J. Wood, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, New York), p. 245.
J. Oitmaa and D. Betts,Can. J. Phys. 56:897 (1978).
H. Q. Lin and J. E. Hirsch, to be published.
J. E. Hirsch,Phys. Rev. Lett. 54:1317 (1985).
J. E. Hirsch and D. J. Scalapino, to be published.
J. E. Hirsch,Phys. Rev. Lett. 53:2327 (1984);Phys. Rev. B 31:6022 (1985).
H. Q. Lin and J. E. Hirsch,Phys. Rev. B (to be published).
J. E. Hirsch and D. J. Scalapino,Phys. Rev. Lett. 50:1168 (1983);Phys. Rev. B27:7169 (1983);Phys. Rev. B 29:5554 (1984).
J. E. Hirsch,Phys. Rev. Lett. 51:296 (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hirsch, J.E. Simulations of the Hubbard model. J Stat Phys 43, 841–859 (1986). https://doi.org/10.1007/BF02628310
Issue Date:
DOI: https://doi.org/10.1007/BF02628310