Critical behavior with axially correlated random bonds

Critical properties are studied in systems with quenched bond disorder that is correlated along $d_1$ of d dimensions. A renormalization-group scheme (based on the Migdal-Kadanoff method) which follows the full distribution of the random bonds and which gives correctly the modified Harris criterion φ=α+$d_1$ν is used. For $d_1$ q-state Potts models. For $d_1$=d-1 there is no long-range order if there is a finite weight to zero coupling. Otherwise, we find a novel zero-temperature fixed distribution, for which all the moments diverge to infinity with finite ratios among them. This fixed distribution has a magnetic eigenvalue equal to d, indicating a first-order transition in the magnetization and possible related essential singularities. Thus, by analogy, the possibility of a magnetization jump is raised for the McCoy-Wu transition on a square lattice. The results for $d_1$=1 are relevant to random quantum systems.