Supersymmetry approach in the field theory of ergodicity breaking transitions

The supersymmetry (SUSY) self-consistent approximation for the model of non-equilibrium thermodynamic system with quenched disorder is derived from the dynamical action calculated by means of generalized second Legendre transformation technique. The equations for adiabatic and isothermal susceptibilities, memory and field-induced parameters are obtained on the basis of asymptotic analysis of dynamic Dyson equations. It is shown that the marginal stability condition that defines the critical point is governed by fluctuations violating fluctuation–dissipation theorem (FDT). The temperature of ergodicity-breaking transition is calculated as a function of quenched disorder intensities. Transformation of superfields related to the mapping between an instanton process and the corresponding causal solution is discussed.