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Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

by Andrzej Chlebicki, Pawel Jakubczyk

Submission summary

As Contributors: Andrzej Chlebicki · Pawel Jakubczyk
Arxiv Link: https://arxiv.org/abs/2012.00782v3 (pdf)
Date submitted: 2020-12-10 09:57
Submitted by: Chlebicki, Andrzej
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
  • Statistical and Soft Matter Physics
Approach: Theoretical

Abstract

We employ the functional renormalization group framework at 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 Cardy-Hamber 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 $\nu^{-1}(d,N)$ we find 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. We provide a discussion of the evolution of the obtained picture upon varying $d$ and $N$ between $(d,N)=(2,2)$ and other, earlier studied cases, such as $d\to 3$ or $N\to \infty$.

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Submission 2012.00782v3 on 10 December 2020

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