Coulomb blockade in metallic grains at large conductance: beyond the zero-dimensional limit

We consider mesoscopic fluctuations of the Coulomb blockade oscillations in a disordered metallic grain in an external magnetic field coupled to a metallic lead by a tunneling contact with a large conductance $g_T$ and capacitively coupled to a gate. For a finite mean level spacing $\delta$ in the grain and at temperatures $T \gg \delta$ we obtain the oscillatory part of the correlator of thermodynamic potentials at different values of the gate voltage. The correlations decay algebraically with the gate voltage difference in contrast to the exponential decay that would result from the mean-field treatment of the Coulomb interaction. The results are valid beyond the zero-dimensional limit and describe the crossover between the unitary and orthogonal ensembles.