Nonextensive percolation and Lee-Yang edge singularity from nonextensive $\lambda\phi^{3}$ scalar field theory

TL;DR

This paper calculates nonextensive critical exponents for a scalar field theory, extending percolation and Lee-Yang problems to systems with global correlations, and shows how these exponents depend on the nonextensive parameter q.

Contribution

It introduces a nonextensive statistical field theory approach to compute critical exponents for $bb\u03b3$ scalar field theory, generalizing known results to include nonextensive effects.

Findings

Critical exponents depend on the nonextensive parameter q.

Extensive results are recovered as q approaches 1.

The nonextensive exponents align with the universality hypothesis.

Abstract

We compute the critical exponents for nonextensive $\lambda\phi^{3}$ scalar field theory for all loop orders and $|q - 1| < 1$. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding systems are nonextensive generalizations of their extensive counterparts. For that we employ tools from the recently introduced nonextensive statistical field theory. The results for the nonextensive critical exponents computed depend on the nonextensive parameter $q$, which encodes global correlations among the degrees of freedom of the system. The extensive results are recovered in the limit $q\rightarrow 1$. There is an interplay between global correlations and fluctuations, once the nonextensive critical exponents depend on $q$. This dependence is in agreement with the universality hypothesis.