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.
Highlights
The Boltzmann-Gibbs theory for describing statistical properties of extensive physical systems has attained a remarkable success [1]
The nonextensive theory is parametrized by a parameter which characterizes the nonextensivity of the theory, namely, the nonextensive parameter q ∈ R
The nonextensive theories for q ≠ 1 but around q 1⁄4 1 are obtained as the first-order Taylor expansion of their nonextensive counterparts for q ≠ 1 but away from q 1⁄4 1 in the region q ∼ 1
Summary
The Boltzmann-Gibbs theory for describing statistical properties of extensive physical systems has attained a remarkable success [1]. The aim of this work is to investigate the nonextensivity of the OðNÞ λφ scalar high energy nonextensive q-field theory through the computation of the all-loop radiative quantum corrections, after a finite next-to-leading-order (NLO) evaluation, for dimensions 2 < d < 4 through ε-expansion techniques in ε 1⁄4 4 − d to the high energy nonextensive universal critical exponents and amplitude. We apply the fieldtheoretic renormalization group approach [11] In this approach, when the system is undergoing a continuous phase transition, its critical behavior is a result of the fluctuating properties of a fluctuating quantum field φ whose mean value is associated to the order parameter (magnetization for magnetic systems, for example). This work is organized as follows: Firstly, we have to compute the radiative quantum corrections to the high energy nonextensive critical exponents up to NLO through six distinct and independent renormalization methods for OðNÞ λφ scalar high energy nonextensive q-field theories. Compute the high energy nonextensive critical exponents through the methods displayed below
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