Nonextensive statistical field theory

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.

arXiv commentSubmitted to Journal on November-23-2021, 5 pages, IX Tables

References in corpus (19)

• Thermostatistics of overdamped motion of interacting particles
• Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
• From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar{p}$ collisions
• Experimental validation of nonextensive scaling law in confined granular media
• Is Tsallis thermodynamics nonextensive?
• Magnetic phase diagram for a non-extensive system: Experimental connection with manganites
• Magnetic behavior of a non-extensive S-spin system: possible connections to manganites
• A new picture of the Lifshitz critical behavior
• Evidences for Tsallis non-extensivity on CMR manganites
• Thermodynamic properties and transport coefficients of QCD matter within the non-extensive Polyakov-Nambu-Jona-Lasinio model
• Experimental determination of the non-extensive entropic parameter $q$
• Generalization of the possible algebraic basis of $q$-triplets
• Finite size analysis of a two-dimensional Ising model within a nonextensive approach
• Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories
• QCD phase diagram and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model
• Computation of the dynamic critical exponent of the three-dimensional Heisenberg model
• Tsallis' Quantum q-Fields
• Diffeomorphism symmetry effect on the O(N ) universality class
• Critical exponents and amplitude ratios of scalar nonextensive $q$-field theories

Cited by in corpus (3)

• Experimental validation of nonextensive statistical field theory: applications to manganites
• Is Kaniadakis $\kappa$-generalized statistical mechanics general?
• Nonextensive percolation and Lee-Yang edge singularity from nonextensive $\lambda {\varphi }^3$ scalar field theory