Nonextensive statistical field theory

TL;DR

This paper develops a field-theoretic framework to analyze nonextensive systems with global correlations, deriving universal critical exponents for O(N) models that depend on the nonextensive parameter q, and validating results with simulations.

Contribution

It introduces the first analytical computation of q-dependent critical exponents for nonextensive O(N) models, establishing a new universality class and demonstrating the method's broad applicability.

Findings

Derived universal static and dynamic q-dependent critical exponents.

Validated analytical results with computer simulations for 2D Ising systems.

Established a new nonextensive O(N)$_{q}$ universality class.

Abstract

We introduce a field-theoretic approach for describing the critical behavior of nonextensive systems, systems displaying global correlations among their degrees of freedom, encoded by the nonextensive parameter $q$. As some applications, we report, to our knowledge, the first analytical computation of both universal static and dynamic $q$-dependent nonextensive critical exponents for O($N$) vector models, valid for all loop orders and $|q - 1| < 1$. Then emerges the new nonextensive O($N$)$_{q}$ universality class. We employ six independent methods which furnish identical results. Particularly, the results for nonextensive 2d Ising systems, exact within the referred approximation, agree with that obtained from computer simulations, within the margin of error, as better as $q$ is closer to $1$. We argue that the present approach can be applied to all models described by extensive statistical field theory as well. The results show an interplay between global correlations and fluctuations.