Analytical study of fermion determinant and chiral condensate behavior at finite temperatures in toy model approximation

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 $arediscarded$.$ Chiral condensate is studied in the area of small ($m<<T$) quark masses.