SCALING NEAR RANDOM CRITICALITY IN 2-DIMENSIONAL DIRAC FERMIONS

Recently the existence of a random critical line in two-dimensional Di rac fermions was confirmed. In this paper, we focus on its scaling pro perties, especially in the critical region. We treat Dirac fermions in two dimensions with two types of randomness, a random site (RS) model and a random hopping (RH) model. The RS model belongs to the usual or thogonal class and all states are localized. For the RH model, there i s an additional symmetry expressed by {H, y}=0. Therefore, although al l nonzero energy states localize, the localization length diverges at the zero energy. In the weak localization region, the generalized Ohm' s law in fractional dimensions, d(<2), has been observed for the RH m odel.