  Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite
volume can be seen in a finite box by studying, for instance, the dependence of
the chiral condensate from the volume and the quark mass. We perform a
feasibility study of this program by computing the quark condensate on the
lattice in the quenched approximation of QCD at small quark masses. We carry
out simulations in various topological sectors of the theory at several
volumes, quark masses and lattice spacings by employing fermions with an exact
chiral symmetry, and we focus on observables which are infrared stable and free
from mass-dependent ultraviolet divergences. The numerical calculation is
carried out with an exact variance-reduction technique, which is designed to be
particularly efficient when spontaneous symmetry breaking is at work in
generating a few very small low-lying eigenvalues of the Dirac operator. The
finite-size scaling behaviour of the condensate in the topological sectors
considered agrees, within our statistical accuracy, with the expectations of
the chiral effective theory. Close to the chiral limit we observe a detailed
agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the
volume and the topology dependence of our results with the predictions of the
chiral effective theory, we extract the corresponding low-energy constant.
