We argue that massless Dirac particles in two spatial dimensions with $1∕r$ Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of Herbut, Juricic, and Vafek [arXiv:0707.4171 (unpublished)]. At small interaction and small randomness, there is an infrared stable fixed curve which merges with the strongly interacting infrared unstable line at a critical endpoint, along which the dynamical critical exponent $z=1$.

• Received 21 October 2007

DOI:https://doi.org/10.1103/PhysRevB.77.033410