We use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field. A fixed point stable below dc= 5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in e = 5 - d. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents.