  Using a new cluster Monte Carlo algorithm, we study the phase diagram and
critical properties of an interacting pair of resistively shunted Josephson
junctions. This system models tunneling between two electrodes through a small
superconducting grain, and is described by a double sine-Gordon model. In
accordance with theoretical predictions, we observe three different phases and
crossover effects arising from an intermediate coupling fixed point. On the
superconductor-to-metal phase boundary, the observed critical behavior is
within error-bars the same as in a single junction, with identical values of
the critical resistance and a correlation function exponent which depends only
on the strength of the Josephson coupling. We explain these critical properties
on the basis of a renormalization group (RG) calculation. In addition, we
propose an alternative new mean-field theory for this transition, which
correctly predicts the location of the phase boundary at intermediate Josephson
coupling strength.
