  We consider long, finite-width strips of Ising spins with randomly
distributed couplings. Frustration is introduced by allowing both ferro- and
antiferromagnetic interactions. Free energy and spin-spin correlation functions
are calculated by transfer-matrix methods. Numerical derivatives and
finite-size scaling concepts allow estimates of the usual critical exponents
$\gamma/\nu$, $\alpha/\nu$ and $\nu$ to be obtained, whenever a second-order
transition is present. Low-temperature ordering persists for suitably small
concentrations of frustrated bonds, with a transition governed by pure--Ising
exponents. Contrary to the unfrustrated case, subdominant terms do not fit a
simple, logarithmic-enhancement form. Our analysis also suggests a vertical
critical line at and below the Nishimori point. Approaching this point along
either the temperature axis or the Nishimori line, one finds non-diverging
specific heats. A percolation-like ratio $\gamma/\nu$ is found upon analysis of
the uniform susceptibility at the Nishimori point. Our data are also consistent
with frustration inducing a breakdown of the relationship between
correlation-length amplitude and critical exponents, predicted by conformal
invariance for pure systems.
