Analyticity of critical exponents of the O(N) models from nonperturbative renormalization
Abstract
We employ the functional renormalization group framework at the second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. We in particular address the CardyHamber prediction concerning nonanalytical behavior of the critical exponents $\nu$ and $\eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $\eta(d,N)$ and $\nu^{1}(d,N)$ as well as analysis of the functional fixedpoint profiles, we find clear indications of this line in the form of a crossover between two regimes in the $(d,N)$ plane, however no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $\eta(d,N)$ and $\nu^{1}(d,N)$ become increasingly large for $d\to 2$ and $N\to 2$ and it is only in this limit that $\eta(d,N)$ and $\nu^{1}(d,N)$ as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on $N$ for $d>2$ we find no indication of its vanishing as anticipated by the CardyHamber scenario. For dimensionality $d$ approaching 3 there are no signatures of the CardyHamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.
 Publication:

SciPost Physics
 Pub Date:
 June 2021
 DOI:
 10.21468/SciPostPhys.10.6.134
 arXiv:
 arXiv:2012.00782
 Bibcode:
 2021ScPP...10..134C
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 Submission to SciPost, 24 pages, 12 figures