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We consider a clean two-dimensional interacting electron gas subject to arandom perpendicular magnetic field, h({\bf r}). The field is nonquantizing, inthe sense, that {\cal N}_h-a typical flux into the area \lambda_{\text{\tinyF}}^2 in the units of the flux quantum (\lambda_{\text{\tiny F}} is the deBroglie wavelength) is small, {\cal N}_h\ll 1. If the spacial scale, \xi, ofchange of h({\bf r}) is much larger than \lambda_{\text{\tiny F}}, theelectrons move along semiclassical trajectories. We demonstrate that a weakfield-induced curving of the trajectories affects the interaction-inducedelectron lifetime in a singular fashion: it gives rise to the correction to thelifetime with a very sharp energy dependence. The correction persists withinthe interval \omega \sim \omega_0= E_{\text{\tiny F}}{\cal N}_h^{2/3} muchsmaller than the Fermi energy, E_{\text{\tiny F}}. It emerges in the thirdorder in the interaction strength; the underlying physics is that a small phasevolume \sim (\omega/E_{\text{\tiny F}})^{1/2} for scattering processes,involving {\em two} electron-hole pairs, is suppressed by curving. Even moresurprising effect that we find is that {\em disorder-averaged} interactioncorrection to the density of states, \delta\nu(\omega), exhibits {\emoscillatory} behavior, periodic in \bigl(\omega/\omega_0\bigr)^{3/2}. In ourcalculations of interaction corrections random field is incorporated via thephases of the Green functions in the coordinate space. We discuss the relevanceof the new low-energy scale for realizations of a smooth random field incomposite fermions and in disordered phase of spin-fermion model offerromagnetic quantum criticality.

Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point