  A binary liquid near its consolute point exhibits critical fluctuations of
the local composition; the diverging correlation length has always challenged
simulations. The method of choice for the calculation of critical points in the
phase diagram is a scaling analysis of finite-size corrections, based on a
sequence of widely different system sizes. Here, we discuss an alternative
using cubic sub-systems of one large simulation as facilitated by modern,
massively parallel hardware. We exemplify the method for a symmetric binary
liquid at critical composition and compare different routes to the critical
temperature: (1) fitting the critical divergences of the correlation length and
the susceptibility encoded in the composition structure factor of the whole
system, (2) testing data collapse and scaling of moments of the composition
fluctuations in sub-volumes, and (3) applying the cumulant intersection
criterion to the sub-systems. For the last route, two difficulties arise:
sub-volumes are open systems with free boundary conditions, for which no
precise estimate of the critical Binder cumulant $U_c$ is available. Second,
the periodic boundaries of the simulation box interfere with the sub-volumes,
which we resolve by a two-parameter finite-size scaling. The implied
modification to the data analysis restores the common intersection point, and
we estimate $U_c=0.201 \pm 0.001$, universal for cubic Ising-like systems with
free boundaries. Confluent corrections to scaling, which arise for small
sub-system sizes, are quantified at leading order and our data for the critical
susceptibility are compatible with the universal correction exponent
$\omega\approx 0.83$.
