Statistical theory of self-similarly distributed fields

Abstract

A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivate. With such a choice, the role of a fluctuating order parameter is shown to play deformed logarithm of the amplitude of a hydrodynamic mode. Within the harmonic approach, deformed partition function and moments of the order parameter of lowers powers are found. A set of equations for the generating functional is obtained to take into account constrains and symmetry of the statistical system. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2729