  We study peculiarities of transport through a Coulomb blockade system tuned
to the vicinity of the spin transition in its ground state. Such transitions
can be induced in practice by application of a magnetic field. Tunneling of
electrons between the dot and leads mixes the states belonging to the ground
state manifold of the dot. Remarkably, both the orbital and spin degrees of
freedom of the electrons are engaged in the mixing at the singlet-triplet
transition point. We present a model which provides an adequate theoretical
description of recent experiments with semiconductor quantum dots and carbon
nanotubes.
