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

@article{Chlebicki2020AnalyticityOC,
title={Analyticity of critical exponents of the \$O(N)\$ models from nonperturbative renormalization},
author={Andrzej Chlebicki and Paweł Jakubczyk},
journal={arXiv: Statistical Mechanics},
year={2020}
}
• Published 1 December 2020
• Mathematics, Physics
• arXiv: Statistical Mechanics
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 $d$. Of our special interest are phenomena occurring in the vicinity of $d=2$. 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 $(2,2… 3 Citations ## Figures from this paper My title A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in [1]. Its efficacy was demonstrated in the simplest example possible, i.e. that Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group • Physics Physical Review D • 2022 We investigate the massive Schwinger model in d = 1 + 1 dimensions using bosonization and the non-perturbative functional renormalization group. In agreement with previous studies we find that the Perturbative and nonperturbative studies of CFTs with MN global symmetry • Physics SciPost Physics • 2021 <jats:p>Fixed points in three dimensions described by conformal field theories with <jats:inline-formula><jats:alternatives><jats:tex-math>\ensuremath{M N}_{m,n} = O(m)^n\rtimes ## References SHOWING 1-10 OF 54 REFERENCES Nonperturbative renormalization group treatment of amplitude fluctuations for |φ | 4 topological phase transitions • Physics • 2017 The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional${|\ensuremath{\varphi}|}^{4}$models can be performed in several representations, and the amplitude-phase (AP) Madelung Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: Irrelevance of amplitude and out-of-plane fluctuations. • Physics Physical review. E • 2017 A functional renormalization group (FRG) approach for the two-dimensional XY model is developed by combining the lattice FRG proposed by Machado and Dupuis with a duality transformation that explicitly introduces vortices via an integer-valued field, demonstrating that previous failures to obtain a line of true fixed points within the FRG are a mathematical artifact of insufficient truncation schemes. Critical exponents of O (N ) models in fractional dimensions • Mathematics • 2015 We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition • Physics • 2001 The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two-dimensional${\ensuremath{\varphi}}^{4}$model. The observation of essential scaling Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase • Physics • 2017 We analyze the interplay of longitudinal and transverse fluctuations in a$U(1)$symmetric two-dimensional$\phi^4\$-theory. To this end, we derive coupled renormalization group equations for both
Unified picture of ferromagnetism, quasi-long-range order, and criticality in random-field models.
• Physics
Physical review letters
• 2006
The interplay between ferromagnetism, quasi-long-range order (QLRO), and criticality in the d-dimensional random-field O(N) model in the whole (N, d) diagram is studied.