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

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.