# 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} }

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

My title

- Mathematics
- 2022

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

- PhysicsPhysical 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

- PhysicsSciPost 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.

- PhysicsPhysical 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.

- PhysicsPhysical 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.