Phase transitions in relativistic models induced by a stochastic potential

The vacuum response to an external static scalar and pseudoscalar stochastic field is investigated. A new (stochastic) mechanism of mass generation is suggested for four-dimensional model of interacting massless scalar and fermion fields. The mean density of states of Dirac fermions in the “pseudoscalar white noise” is calculated exactly in two-dimensional space-time. It is shown that the rapidly varying stochastic field enhances the threshold singularity in the density of states and gives rise to the stimulation (increase) of the effective fermion mass.