On the completeness of the $\delta_{KLS}$-generalized statistical field theory

TL;DR

This paper introduces a generalized statistical field theory using the $oldsymbol{ extdelta_{KLS}}$ parameter to evaluate critical exponents in systems undergoing phase transitions, revealing new universality classes with limitations in describing real materials.

Contribution

It develops a $oldsymbol{ extdelta_{KLS}}$-generalized statistical field theory extending Boltzmann-Gibbs, providing insights into critical exponents and universality classes, and analyzing their physical interpretation and limitations.

Findings

New generalized universality classes emerge.

Generalized theory recovers Boltzmann-Gibbs in the limit.

Incomplete description of some real materials.

Abstract

In this work we introduce a field-theoretic tool that enable us to evaluate the critical exponents of $\delta_{KLS}$-generalized systems undergoing continuous phase transitions, namely $\delta_{KLS}$-generalized statistical field theory. It generalizes the standard Boltzmann-Gibbs through the introduction of the $\delta_{KLS}$ parameter from which Boltzmann-Gibbs statistics is recovered in the limit $\delta_{KLS}\rightarrow 0$. From the results for the critical exponents we provide the referred physical interpretation for the $\delta_{KLS}$ parameter. Although new generalized universality classes emerge, we show that they are incomplete for describing the behavior of some real materials. This task is fulfilled only for nonextensive statistical field theory, which is related to fractal derivative and multifractal geometries, up to the moment, for our knowledge.