Critical exponents and amplitude ratios of scalar nonextensive $q$-field theories

TL;DR

This paper calculates critical exponents and amplitude ratios in high energy nonextensive scalar field theories, showing they match their extensive low energy counterparts, indicating nonextensivity breaks down at high energies.

Contribution

It provides a comprehensive calculation of high energy nonextensive critical exponents and amplitude ratios using multiple methods, demonstrating their universality and equivalence to extensive results.

Findings

High energy nonextensive critical exponents are consistent across methods.

Amplitude ratios are also universal and method-independent.

Nonextensivity effects vanish at high energies, matching extensive theory results.

Abstract

We compute the radiative quantum corrections to the critical exponents and amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar high energy nonextensive $q$-field theories. We employ the field theoretic renormalization group approach through six methods for evaluating the high energy nonextensive critical exponents up to next-to-leading order while the high energy nonextensive amplitude ratios are computed up to leading level by applying three methods. Later we generalize these high energy nonextensive finite loop order results for any loop level. We find that the high energy nonextensive critical exponents are the same when obtained through all the methods employed. The same fact occurs for the high energy nonextensive amplitude ratios. Furthermore, we show that these high energy nonextensive universal quantities are equal to their low energy extensive counterparts, thus showing that the nonextensivity is broken down at high energies.