Statistical theory of self-similarly distributed fields

Details Statistical theory of self-similarly distributed fields Statistical theory of self-similarly distributed fields

2009-09-28

arxiv.org/abs/0909.5142v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 figures. Accepted for publication in Physics Letters A. DOI 10.1016/j.physleta.2009.08.070

Scientific paper

10.1016/j.physleta.2009.08.070

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 derivative. 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 lower powers are found. A set of equations for the generating functional is obtained to take into account constraints and symmetry of the statistical system.

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