  The random-bond Ising model on the square lattice has several disordered
critical points, depending on the probability distribution of the bonds. There
are a finite-temperature multicritical point, called Nishimori point, and a
zero-temperature fixed point, for both a binary distribution where the coupling
constants take the values +/- J and a Gaussian disorder distribution. Inclusion
of dilution in the +/- J distribution (J=0 for some bonds) gives rise to
another zero-temperature fixed point which can be identified with percolation
in the non-frustrated case (J >= 0). We study these fixed points using
numerical (transfer matrix) methods. We determine the location, critical
exponents, and central charge of the different fixed points and study the
spin-spin correlation functions. Our main findings are the following: (1) We
confirm that the Nishimori point is universal with respect to the type of
disorder, i.e. we obtain the same central charge and critical exponents for the
+/- J and Gaussian distributions of disorder. (2) The Nishimori point, the
zero-temperature fixed point for the +/- J and Gaussian distributions of
disorder, and the percolation point in the diluted case all belong to mutually
distinct universality classes. (3) The paramagnetic phase is re-entrant below
the Nishimori point, i.e. the zero-temperature fixed points are not located
exactly below the Nishimori point, neither for the +/- J distribution, nor for
the Gaussian distribution.
