  We use numerical transfer-matrix methods to investigate properties of the
multicriticalpoint of binary Ising spin glasses on a square lattice, whose
location we assume to be given exactly by a conjecture advanced by Nishimori
and Nemoto. We calculate the two largest Lyapunov exponents, as well as linear
and non-linear zero-field uniform susceptibilities, on strip of widths $4 \leq
L \leq 16$ sites, from which we estimate the conformal anomaly $c$, the
decay-of-correlations exponent $\eta$, and the linear and non-linear
susceptibility exponents $\gamma/\nu$ and $\gamma^{nl}/\nu$, with the help of
finite-size scaling and conformal invariance concepts. Our results are:
$c=0.46(1)$; $0.187 \lesssim \eta \lesssim 0.196$; $\gamma/\nu=1.797(5)$;
$\gamma^{nl}/\nu=5.59(2)$. A direct evaluation of correlation functions on the
strip geometry, and of the statistics of the zeroth moment of the associated
probability distribution, gives $\eta=0.194(1)$, consistent with the
calculation via Lyapunov exponents. Overall, these values tend to be
inconsistent with the universality class of percolation, though by small
amounts. The scaling relation $\gamma^{nl}/\nu=2 \gamma/\nu+d$ (with space
dimensionality $d=2$) is obeyed to rather good accuracy, thus showing no
evidence of multiscaling behavior of the susceptibilities.
