arXiv subjects

Nicolás Wschebor

Publications and source records attributed to Nicolás Wschebor.

At least 19 recordsLinked to original sources

arXiv2026

Conformal Invariance of the large-$N$ limit of the $O(N)$ universality class

Conformal symmetry is expected to be realized in many equilibrium statistical mechanical systems at criticality. Although this is certainly true in two-dimensional systems, the three-dimensional case is subtler, and only a few proofs exist, only so in very specific cases. In this work, we give two proofs for the large $N$ limit of the $O(N)$ universality class within the non-perturbative renormalization group framework: one functional, and one vertex-by-vertex in Fourier space. While doing so, we unveil how the theory is structured in order for conformal symmetry to be realized. As a consequence, we shed light on what to expect, on rather general grounds, for a theory to be conformally invariant.

cond-mat.stat-mech↗

arXiv2026

Scaling regimes of the Kuramoto-Sivashinsky equation from the functional renormalization group

We revisit the renormalization group (RG) approach to the one-dimensional stochastic Kuramoto-Sivashinsky (KS) equation and show that previous approaches based on perturbative Wilsonian RG with a sharp cutoff are not valid, even though they yield a qualitatively correct picture. The reason is that taking momentum derivatives while using the sharp cutoff is not well-defined in some cases and leads to intrinsic divergencies. This is a well-known problem of Wilsonian RG, which can be simply cured by using a smooth cutoff, and employing the functional renormalization group (FRG) framework. We establish the flow equations for the KS model within the FRG, and demonstrate that it flows to the Kardar-Parisi-Zhang (KPZ) fixed point at large scales. We then calculate the full two-point correlation function over a wide range of momenta and frequencies. We show that it exhibits three universal scaling regimes that we characterize: the KPZ regime (with dynamical exponent $z=3/2$), the Edwards-Wilkinson regime (with $z=2$) and the recently discovered inviscid regime (with $z=1$). The latter develops over an extended range of large wavenumbers and originates from the vanishing of the effective viscosity. Lastly, we investigate the large-scale behavior of the deterministic KS equation by studying the limit of vanishing noise and we determine the scales where the KPZ regime can emerge in the deterministic case.

cond-mat.stat-mech↗

arXiv2026

Inviscid scaling in the Kuramoto-Sivashinsky equation from functional renormalization group and direct numerical simulations

We show that the one-dimensional Kuramoto-Sivashinsky (KS) equation features a scaling regime characterized by the dynamical exponent $z=1$ at intermediate scales between the large-scale Kardar-Parisi-Zhang (KPZ) scaling with $z=3/2$ and the small-scale non-universal behavior. This scaling regime is intrinsic to the KS dynamics since it arises from the vanishing of the effective viscosity when evolving from its microscopic negative KS value, to its macroscopic effective positive KPZ value. This vanishing of the viscosity deeply imprints the behavior of correlations at intermediate scales, which exhibit a universal $z=1$ scaling. This behavior pertains to the inviscid-Burgers universality class, which corresponds to the zero-viscosity fixed point of the KPZ equation. We evidence and characterize this so-far-overlooked scaling regime using both functional renormalization group and direct numerical simulations.

cond-mat.stat-mech↗

arXiv2025

Unveiling the different scaling regimes of the one-dimensional Kardar-Parisi-Zhang--Burgers equation using the functional renormalisation group

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported in recent numerical simulations. This new regime is characterised by a dynamical exponent $z=1$, markedly different from the expected one $z=3/2$ for the KPZ universality class, and it emerges when approaching the inviscid limit. The origin of this scaling has been traced down to the existence of a new fixed point, termed the inviscid Burgers (IB) fixed point, which was uncovered using the functional renormalisation group (FRG). The FRG equations can be solved analytically in the asymptotic regime of vanishing viscosity and large momenta, showing that indeed $z=1$ exactly at the IB fixed point. In this work, we set up an advanced method to numerically solve the full FRG flow equations in a certain approximation, which allows us to determine in a unified way the correlation function over the whole range of momenta, not restricted to some particular regime. We analyse the crossover between the different fixed points, and quantitatively determine the extent of the IB regime.

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arXiv2025

Scenario for quark confinement from infrared safe Yang-Mills dynamics

We revisit the non-Abelian dipole problem in the context of a simple semiclassical approach that incorporates some essential features of the infrared sector of Yang-Mills theories in the Landau gauge, in particular, the fact that both the running coupling and the gluon propagator remain finite at infrared scales and that the latter shows positivity violations that reflects the presence of massless modes. We obtain a simple flux tube solution in a controlled approximation scheme, which we compare to the results of lattice simulations.

hep-th↗

arXiv2024

Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group

The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often required, and the framework of the nonperturbative, or functional renormalization group is no exception. The derivative expansion is one of the most popular approximation schemes within this framework, due to its great performance on multiple systems, as evidenced in the last decades. Nevertheless, it has the downside of breaking conformal symmetry at a finite order. This breaking is not observed at the leading order of the expansion, denoted LPA approximation, and only appears once one considers, at least, the next-to-leading order of the derivative expansion ($\mathcal{O}(\partial^2)$) when including composite operators. In this work, we study the constraints arising from conformal symmetry for the $O(N)$ models using the derivative expansion at order $\mathcal{O}(\partial^2)$. We explore various values of $N$ and minimize the breaking of conformal symmetry to fix the non-physical parameters of the approximation procedure. We compare our prediction for the critical exponents with those coming from a more usual procedure, known as the principle of minimal sensitivity.

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arXiv2024

The inviscid fixed point of the multi-dimensional Burgers-KPZ equation

A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing from the well-known KPZ one $z=3/2$, was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated. It was shown to be controlled by a yet unpredicted fixed point of the one-dimensional Burgers-KPZ equation, termed inviscid Burgers (IB) fixed point. The associated universal properties, including the scaling function, were calculated. All these findings were restricted to $d=1$, and it raises the intriguing question of the fate of this new IB fixed point in higher dimensions. In this work, we address this issue and analyze the multi-dimensional Burgers-KPZ equation using functional renormalization group. We show that the IB fixed point exists in all dimensions $d\geq 0$, and that it controls the large momentum behavior of the correlation functions in the inviscid limit. It turns out that it yields in all $d$ the same super-universal value $z=1$ for the dynamical exponent.

cond-mat.stat-mech↗

arXiv2024

$O(N)\times O(2)$ scalar models: including $\mathcal{O}(\partial^2)$ corrections in the Functional Renormalization Group analysis

The study of phase transitions in frustrated magnetic systems with $O(N)\times O(2)$ symmetry has been the subject of controversy for more than twenty years, with theoretical, numerical and experimental results in disagreement. Even theoretical studies lead to different results, with some predicting a first-order phase transition while others find it to be second-order. Recently, a series of results from both numerical simulations and theoretical analyses, in particular those based on the Conformal Bootstrap, have rekindled interest in this controversy, especially as they are still not in agreement with each other. Studies based on the functional renormalization group have played a major role in this controversy in the past, and we revisit these studies, taking them a step further by adding non-trivial second order derivative terms to the derivative expansion of the effective action. We confirm the first-order nature of the phase transition for physical values of $N$, i.e. for $N=2$ and $N=3$ in agreement with the latest results obtained with the Conformal Bootstrap. We also study an other phase of the $O(N)\times O(2)$ models, called the sinusoidal phase, qualitatively confirming earlier perturbative results.

cond-mat.stat-mech↗

arXiv2024

Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the non-perturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the Derivative Expansion (DE), non-trivial constraints only apply from third order (usually denoted $\mathcal{O}(\partial^4)$), at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work, we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE (or $\mathcal{O}(\partial^2)$). We show how these constraints can be used to fix nonphysical regulator parameters.

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arXiv2023

The $q-$state Potts model from the Nonperturbative Renormalization Group

We study the $q$-state Potts model for $q$ and the space dimension $d$ arbitrary real numbers using the Derivative Expansion of the Nonperturbative Renormalization Group at its leading order, the local potential approximation (LPA and LPA'). We determine the curve $q_c(d)$ separating the first ($q>q_c(d)$) and second ($q<q_c(d)$) order phase transition regions for $2.8<d\leq 4$. At small $ε=4-d$ and $δ=q-2$ the calculation is performed in a double expansion in these parameters and we find $q_c(d)=2+a ε^2$ with $a\simeq 0.1$. For finite values of $ε$ and $δ$, we obtain this curve by integrating the LPA and LPA' flow equations. We find that $q_c(d=3)=2.11(7)$ which confirms that the transition is of first order in $d=3$ for the three-state Potts model.

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arXiv2022

Small parameters in infrared QCD: The pion decay constant

We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the dynamics of chiral symmetry breaking at the level of the quark propagator and, in particular, the dynamical generation of a constituent quark mass. In the present article, we study the associated Goldstone mode, the pion, and we compute the pion decay constant in the chiral limit. Our approach exploits the fact that the coupling (defined in the Taylor scheme) in the pure gauge sector is perturbative, as observed in lattice simulations which, together with a $1/N_c$-expansion, allows for a systematic, controllable approximation scheme in the low energy regime of QCD. At leading order, this leads to the well-known rainbow-ladder resummation. We study the region of parameter space of the model that gives physical values of the pion decay constant. This allows one to constrain the gluon mass parameter as a function of the coupling using a physically measured quantity.

hep-ph↗

arXiv2022

$\mathbb{Z}_4$-symmetric perturbations to the XY model from functional renormalization

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic ($\mathbb{Z}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O(2)$-symmetric and $\mathbb{Z}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

cond-mat.stat-mech↗

arXiv2022

The regulator dependence in the functional renormalization group: a quantitative explanation

The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory. In particular, the most employed approximation scheme in this context, the derivative expansion, was recently shown to converge and yield accurate and very precise results. However, this convergence strongly depends on the shape of the employed regulator. In this letter we clarify the reason for this dependence and justify, simultaneously, the most largely employed procedure to fix this dependence, the principle of minimal sensitivity.

cond-mat.stat-mech↗

arXiv2021

Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling

We investigate the spontaneous breaking of chiral symmetry in QCD by means of a recently proposed approximation scheme in the Landau-gauge Curci-Ferrari model, which combines an expansion in the Yang-Mills coupling and in the inverse number of colors, without expanding in the quark-gluon coupling. The expansion allows for a consistent treatment of ultraviolet tails via renormalization group techniques. At leading order, it leads to the resummation of rainbow diagrams for the quark propagator, with, however, a trivial running of both the gluon mass and the quark-gluon coupling. In a previous work, by using a simple model for a more realistic running of these parameters, we could reproduce the known phenomenology of chiral symmetry breaking, including a satisfactory description of the lattice data for the quark mass function. Here, we get rid of this model-dependence by taking our approximation scheme to next-to-leading order. This allows us to consistently include the realistic running of the parameters and to access the unquenched gluon and ghost propagators to first nontrivial order, which we can compare to available lattice data for an even more stringent test of our approach. In particular, our results for the various two-point functions compare well with lattice data while the parameters of the model are strongly constrained.

hep-ph↗

arXiv2021

Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}(\partial^4)$

In the last few years the derivative expansion of the Non-Perturbative Renormalization Group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of its convergence properties allowed for an estimate of the error bars as well as the precise computation of many critical quantities. In this work we extend previous studies to the computation of several universal amplitude ratios for the critical regime of $O(N)$ models using the derivative expansion of the Non-Perturbative Renormalization Group at order $\mathcal{O}(\partial^4)$ for three dimensional systems.

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arXiv2021

A window on infrared QCD with small expansion parameters

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with {\it ab-initio} lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

hep-th↗

arXiv2020

The ghost-antighost-gluon vertex from the Curci-Ferrari model: Two-loop corrections

The Curci-Ferrari model has been shown to provide a good grasp on pure Yang-Mills correlation functions in the Landau gauge, already at one-loop order. In a recent work, the robustness of these results has been tested by evaluating the two-loop corrections to the gluon and ghost propagators. We pursue this systematic investigation by computing the ghost-antighost-gluon vertex to the same accuracy in a particular kinematic configuration that makes the calculations simpler. Because both the parameters of the model and the normalizations of the fields have already been fixed in a previous work, the present calculation represents both a pure prediction and a stringent test of the approach. We find that the two-loop results systematically improve the comparison to Monte-Carlo simulations as compared to earlier one-loop results. The improvement is particularly significative in the SU($3$) case where the predicted ghost-antighost-gluon vertex is in very good agreement with the data. The same comparison in the SU($2$) case is not as good, however. This may be due to the presence of a larger coupling constant in the infrared in that case although we note that a similar mismatch has been quoted in non-perturbative continuum approaches. Despite these features of the SU($2$) case, it is possible to find sets of parameters fitting both the propagators and the ghost-antighost-gluon vertex to a reasonable accuracy.

hep-th↗

arXiv2020

Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator

Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associated with this symmetry is not exactly satisfied. The calculations which best satisfy this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap.

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