  We investigate the critical behavior of the random-bond +- J Ising model on a
square lattice at the multicritical Nishimori point in the T-p phase diagram,
where T is the temperature and p is the disorder parameter (p=1 corresponds to
the pure Ising model). We perform a finite-size scaling analysis of
high-statistics Monte Carlo simulations along the Nishimori line defined by
$2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The
multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and
the renormalization-group dimensions of the operators that control the
multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to
the thermal exponent \nu= 1/y_2=4.00(3) and to the crossover exponent \phi=
y_1/y_2=2.62(6).
