  We have investigated the critical temperature behavior in periodic
superconductor/ ferromagnet (S/F) multilayers as a function of the
ferromagnetic layer thickness $d_f$ and the interface transparency. The
critical temperature $T_c(d_f)$ exhibits a damped oscillatory behavior in these
systems due to an exchange field in the ferromagnetic material. In this work we
have performed $T_c$ calculations using the self-consistent multimode approach,
which is considered to be exact solving method. Using this approach we have
derived the conditions of 0 or $\pi$ state realization in periodic S/F
multilayers. Moreover, we have presented the comparison between the single-mode
and multimode approaches and established the limits of applicability of the
single-mode approximation, frequently used by experimentalists.
