We consider a system of interacting particles, diffusing under the influence of both thermal noise and a random, external electric field which acts in a subspace of m dimensions. In the nonequilibrium steady state, the net current is zero. When the interparticle interaction is short ranged and attractive, a second-order phase transition is expected. Analyzing this system in field-theoretic terms, we find the upper critical dimension to be 4-m and its behavior to fall outside the universality classes of the equilibrium Ising model and the usual driven diffusive system. A new fixed point and critical exponents are computed.