Two-loop approximation in the Coulomb blockade problem

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain connected to a lead by a tunneling contact with a large conductance $g_0$ in a wide temperature range, $E_C{g}_0^4{e}^{-g_0/2\mathrm{}}<T<\mathrm{}{E}_C,$ where $E_C$ is the charging energy. Using the instanton analysis and the renormalization-group approach we obtain our main result, the temperature dependence of the amplitude of CB oscillations, which differs from the previously obtained results. Assuming that at $T<\mathrm{}{E}_C{g}_0^4{e}^{-g_0/2\mathrm{}}$ the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground-state energy as $\propto E_C{g}_0^4{e}^{-g_0/2\mathrm{}}.$