Geodesic
Functional representation of the partition function and phase transitions in the Hubbard model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 102-120 
V. S. Kapitonov. Functional representation of the partition function and phase transitions in the Hubbard model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 12, Tome 209 (1994), pp. 102-120. http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a5/
@article{ZNSL_1994_209_a5,
     author = {V. S. Kapitonov},
     title = {Functional representation of the partition function and phase transitions in the {Hubbard} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--120},
     year = {1994},
     volume = {209},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_209_a5/}
}
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The functional representation of the partition function for the Hubbard model with strong Coulomb repulsion is obtained as integral by auxiliary Grassmann variables. The approximative study of the phase transitions showes: 1) for the small doping constant $\delta$ the system is an antiferromagnetic isolator; 2) for doping $\delta\ge t/U$ the system is a ferromagnetic metal for $U/t>10$, and a superconductor metal for $U/t\lesssim10$. Bibliography: 13 titles.