  Fermion determinant is computed analytically on extremely large lattices $%
N_\tau \to \infty $ in the toy model approximation in which action is truncated
so that in the Hamiltonian limit of $a_\tau \to 0$ all terms of order $a_\tau
/a_\sigma $ are discarded$.$ Chiral condensate is studied in the area of small
($m<<T$) quark masses.
