Is Kaniadakis $\kappa$-generalized statistical mechanics general?

TL;DR

This paper evaluates the $ppa$-generalized statistical field theory's ability to describe critical phenomena in systems like imperfect crystals, concluding it is not sufficiently general and should be discarded as a universal approach.

Contribution

The paper introduces a field-theoretic approach for $ppa$-generalized statistics and demonstrates its limitations in modeling critical behavior of real imperfect crystals.

Findings

$ppa$-generalized systems do not depend on $ppa$

The theory fails to describe critical properties of real imperfect crystals

Alternative nonextensive statistical field theory is more suitable

Abstract

In this Letter we introduce some field-theoretic approach for computing the critical properties of systems undergoing continuous phase transitions governed by the $\kappa$-generalized statistics, namely $\kappa$-generalized statistical field theory. In particular, we show, by computations through analytic and simulation results, that the $\kappa$-generalized Ising-like systems are not capable of describing the nonconventional critical properties of real imperfect crystals, \emph{e. g.} of manganites, as some alternative generalized theory is, namely nonextensive statistical field theory, as shown recently in literature. Although $\kappa$-Ising-like systems do not depend on $\kappa$, we show that a few distinct systems do. Thus the $\kappa$-generalized statistical field theory is not general, \emph{i. e.} it fails to generalize Ising-like systems for describing the critical behavior of imperfect crystals, and must be discarded as one generalizing statistical mechanics. For the latter systems we present the physical interpretation of the theory by furnishing the general physical interpretation of the deformation $\kappa$-parameter.