Journal of Statistical Physics. Vol. 85. Nos. 5/6. 1996. p. 745-761.
We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems — such as the Hubbard model — at half-filling on a general class of graphs. The main ingredient is a procedure which transforms a class of fermionic Hamiltonians into reflection-positive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning the t-V model and an extended Falicov-Kimball model.