Supersymmetry approach in the field theory of ergodicity breaking transitions

TL;DR

This paper develops a supersymmetry-based theoretical framework to analyze ergodicity breaking transitions in non-equilibrium disordered systems, deriving critical conditions and transition temperatures.

Contribution

It introduces a supersymmetry self-consistent approximation for non-equilibrium systems with quenched disorder, linking fluctuations to ergodicity breaking.

Findings

Critical point governed by FDT-violating fluctuations.

Derived temperature of ergodicity breaking as a function of disorder.

Established connection between instanton processes and causal solutions.

Abstract

The supersymmetry 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. The equations for adiabatic and isothermal susceptibilities, memory and field induced parameters are obtained on the basis of asymptotic analysis of dynamical Dyson equations. It is shown that the marginal stability condition that defines the critical point is governed by fluctuations violating 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.