Integration over a superalgebra in the hubbard model with a strong correlation

We represent the partition function of the Hubbard model with a strong Coulomb repulsion as a path integral over auxiliary Grassman variables. An approximate analysis of the phase transitions demonstrates that (1) the system is an antiferromagnetic insulator when the doping constant is small, (2) when t/U, the system is a ferromagnetic metal if U/t > 10, and a superconducting metal if U/t 10.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 269–287, May, 1996.Translated by A. M. Semikhatov.