Diffeomorphism symmetry effect on the O( N ) universality class

Abstract

We probe the effect of diffeomorphism symmetry on the critical exponents values for massive O(N ) λφ 4 scalar field theories in curved spacetime. We apply field-theoretic renormalization group tools, where we use only momentum coordinates as opposed to the earlier standard procedure with both space and momentum coordinates, for computing analytically the critical exponents up to three-loop order for one of them and up to two-loop level for the remaining ones. We found that the curved spacetime critical exponents are the same as their flat spacetime counterparts, at least up to the level considered. At the conclusions we present the physical interpretation for the results.

Influence of conformal symmetry on the amplitude ratios for O(N) models

“…We have to expand the free propagator of the theory and to make our calculations up to linear powers in R and R µν . Also up to linear powers in R and R µν , the present authors performed a computation of the critical exponents in an early work [31]. Now we proceed to obtain the corresponding amplitude ratios.…”

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

“…The critical exponents depend on universal properties of the system as its dimension d, N and symmetry of some N-component order parameter and furthermore if the interactions among their degrees of freedom are of short-or long-range type. They do not depend on nonuniversal properties of the system as its critical temperature, form of its lattice, the nature of spacetime where the field is embedded, as if it is curved [12] or a Lorentz-violating one [13] for example. The nonextensive parameter was physically interpreted as a generalized type of interaction, since they represent the global correlations among the many degrees of freedom of the system.…”

Nonextensive statistical field theory

“…In SFT, the critical indices, for O(N ) vector models, are obtained through the fluctuation properties of some self-interacting fluctuating N -component scalar quantum field φ [5,6]. That properties are its number N of components, the properties of its internal space [25] (the symmetry of that space for example) and the dimension d of the spacetime where the field is embedded but not on the nature of the spacetime itself, as if it is curved [26] or a Lorentz-violating one [27] for example. Aspects like short-and long-range interactions are contained in the form of the free propagators, depending on momentum through quadratic powers [5,6] and other functional forms distinct from quadratic ones [25], respectively.…”