  We study the localization properties of electrons moving on two-dimensional
bi-partite lattices in the presence of disorder. The models investigated
exhibit a chiral symmetry and belong to the chiral orthogonal (chO), chiral
symplectic (chS) or chiral unitary (chU) symmetry class. The disorder is
introduced via real random hopping terms for chO and chS, while complex random
phases generate the disorder in the chiral unitary model. In the latter case an
additional spatially constant, perpendicular magnetic field is also applied.
Using a transfer-matrix-method, we numerically calculate the smallest Lyapunov
exponents that are related to the localization length of the electronic
eigenstates. From a finite-size scaling analysis, the logarithmic divergence of
the localization length at the quantum critical point at E=0 is obtained. We
always find for the critical exponent \kappa, which governs the energy
dependence of the divergence, a value close to 2/3. This result differs from
the exponent \kappa=1/2 found previously for a chiral unitary model in the
absence of a constant magnetic field. We argue that a strong constant magnetic
field changes the exponent \kappa within the chiral unitary symmetry class by
effectively restoring particle-hole symmetry even though a magnetic field
induced transition from the ballistic to the diffusive regime cannot be fully
excluded.
