  Using renormalization-group techniques we analyze equilibrium properties of a
large gated quantum dot coupled via a long and narrow channel to a reservoir of
electrons. Treating the electrons in the channel as one-dimensional and
interacting, we demonstrate that for nearly-open dot and not very strong spin
fluctuations the ground-state properties as a function of the gate voltage are
non-analytic at the points of half-integer average dot population.
Specifically, the exact result of K. A. Matveev, Phys. Rev. B 51, 1743 (1995),
that the dot capacitance shows periodic logarithmic singularities is rederived
as a special case corresponding to non-interacting electrons. We demonstrate
that this conclusion also holds in the presence of SU(2) spin symmetry, and
argue that logarithmic singularities persist as long as the Coulomb blockade is
destroyed which will be the case for sufficiently large tunneling and not very
strong interparticle repulsions. We show that interparticle repulsions aid the
Coulomb blockade to survive disordering effect of zero-point motion provided
the tunneling is sufficiently weak. Upon increase of tunneling, the Coulomb
blockade disappears through a Kosterlitz-Thouless phase transition
characterized by a dot population jump whose magnitude is only determined by
interparticle repulsions in the channel. Similar conclusions are applicable to
systems without SU(2) spin symmetry except that the logarithmic singularity of
the capacitance is replaced by a power-law non-analyticity whose exponent
characterizes the degree of spin fluctuations.
