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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2013 Volume 174, Number 3, Pages 444–466 (Mi tmf8408)

This article is cited in 6 papers

Statistical field theory of a nonadditive system

A. I. Olemskoiab, O. V. Yushchenkob, A. Yu. Badalyanb

a Institute for Applied Physics, Ukrainian AS, , Sumy, Ukraine
b Sumy State University, Sumy, Ukraine

Abstract: Based on quantum field methods, we develop a statistical theory of complex systems with nonadditive potentials. Using the Martin–Siggia–Rose method, we find the effective system Lagrangian, from which we obtain evolution equations for the most probable values of the order parameter and its fluctuation amplitudes. We show that these equations are unchanged under deformations of the statistical distribution while the probabilities of realizing different phase trajectories depend essentially on the nonadditivity parameter. We find the generating functional of a nonadditive system and establish its relation to correlation functions; we introduce a pair of additive generating functionals whose expansion terms determine the set of multipoint Green's functions and their self-energy parts. We find equations for the generating functional of a system having an internal symmetry and constraints. In the harmonic approximation framework, we determine the partition function and moments of the order parameter depending on the nonadditivity parameter. We develop a perturbation theory that allows calculating corrections of an arbitrary order to the indicated quantities.

Keywords: nonadditivity parameter, generating functional, partition function.

Received: 31.08.2012

DOI: 10.4213/tmf8408


 English version:
Theoretical and Mathematical Physics, 2013, 174:3, 386–405

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