Statistical theory of self-similarly distributed fields
Statistical Mechanics
2009-09-29 v1
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 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.
Cite
@article{arxiv.0909.5142,
title = {Statistical theory of self-similarly distributed fields},
author = {Alexander Olemskoi and Irina Shuda},
journal= {arXiv preprint arXiv:0909.5142},
year = {2009}
}
Comments
10 pages, 2 figures. Accepted for publication in Physics Letters A. DOI 10.1016/j.physleta.2009.08.070