Field theory of avalanche formation
  Self-organizing system is studied whose behavior is governed by field of an order parameter, a fluctuation amplitude of conjugate field and a couple of Grassmannian conjugated fields that define the entropy as a control parameter. Within the framework of self-consistent approach the dependencies of macro- and microscopic susceptibilities as well as memory and nonergodicity parameters are determined as a functions of the intensities of thermal and quenched disorders. Making use of the sandpile model shows that proposed scheme determines the conditions of avalanches formation in self-organized criticality phenomena. 
Alexander I. Olemskoi, Alexei V. Khomenko