Quantum critical behavior in gauged Yukawa matrix field theories with quenched disorder

We use the Wilson-Fisher ϵ expansion to study quantum critical behavior in gauged Yukawa matrix field theories with weak quenched disorder. We find that the resulting quantum critical behavior is in the universality class of the pure system. As in the pure system, the phase transition is typically first order, except for a limited range of parameters where it can be second order with computable critical exponents. Our results apply to the study of two-dimensional quantum antiferromagnets with weak quenched disorder and provide an example for fluctuation-induced first order phase transitions in circumstances where naively none are expected.