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Gergely Fejős

Publications and source records attributed to Gergely Fejős.

9 recordsLinked to original sources
arXiv2026

Global Fixed Point Potentials in the Abelian Higgs Model with $N$ flavors

Existence of charged fixed points in the Abelian Higgs model with $N$ flavors in $d$ dimensions is studied using the functional renormalization group. We numerically solve the coupled fixed point equations for the scale dependent charge and the non-perturbative effective potential for the scalar field. We show that the $ε=4-d$ expansion, famously successful in theories with $O(N)$ symmetry, fails to produce reliable results when taking the $ε\rightarrow 1$ limit. By determining global fixed point potentials, it is shown that the critical flavor number at which charged fixed points appear, modifies significantly compared to the perturbative treatment. In $d=3$, signs of a richer fixed point structure with presumably multicritical fixed points are also found. Discussions include subtleties of the gauge fixing and the corresponding modified Ward-Takahashi identities, including the possibility of a nonzero dimensionless photon mass at the infrared fixed point.

hep-ph↗
arXiv2026

FRG analysis of dense two-color QCD within the linear sigma model

We investigate the phase structure, hadron masses, and topological susceptibility in the two-flavor and two-color QCD (QC$_2$D) medium, particularly focusing on the $U(1)_A$ axial anomaly effects. To this end, we employ the linear sigma model, and hadron fluctuations are incorporated through the functional renormalization group method. We establish in detail an effective potential that respects symmetries of QC$_2$D at finite quark chemical potential, $μ_q$: $SU(2)_L\times SU(2)_R$ chiral, $U(1)$ baryon-number, parity and time-reversal symmetries. We find that the $U(1)_A$ anomaly couplings for mesons at finite temperature are enhanced with increasing $μ_q$, while that of the baryons are not too sensitive to $μ_q$. Despite the anomaly enhancement, we find that the topological susceptibility at larger $μ_q$ is always suppressed regardless of the temperature, following chiral restoration. We also find that mass degeneracies of the chiral partners are well realized at higher temperatures and densities by the chiral restoration. Our findings are expected to provide useful information on properties of the $U(1)_A$ anomaly in medium for sign-problem-free lattice simulations of QC$_2$D.

hep-ph↗
arXiv2026

Scaling Behaviors in Active Model B+ via the Functional Renormalization Group

We study the scaling behaviors of the active model B+ using the functional renormalization group (FRG) approach, based on the nonequilibrium effective action formulated via the Martin-Siggia-Rose path-integral formalism. We derive the $β$ functions for all couplings of the system in generic $d$ dimensions, revealing regulator independence in various contributions to the renormalization group (RG) flow at specific values for $d$. After identifying specific regions of the parameter space that define submodels closed under RG transformations, we determine all fixed points of potential physical relevance. We confirm the existence of a bicritical fixed point, which was conjectured within the perturbative momentum-shell RG method for being responsible for the transition from bulk phase separation to microphase separation in active systems. We argue that, within the FRG approach, global flows significantly differ from those obtained in its perturbative counterpart.

cond-mat.stat-mech↗
arXiv2025

Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model

We investigate the thermal properties of hadrons in two-color quantum chromodynamics (QC$_2$D) using the functional renormalization group (FRG) method, with particular focus on modifications of the $U(1)$ axial anomaly effects. The hadrons are described by a linear sigma model (LSM) based on the Pauli-Gürsey $SU(4)$ symmetry, which incorporates both low-lying $0^\pm$ mesons and diquark baryons. We find that all quartic couplings are comparably suppressed when physical values of the pion mass and decay constant are taken as inputs, for which a reasonably smooth chiral symmetry restoration at finite temperature is reproduced. Consequently, mass differences among chiral partners remain small. Despite these tiny mass differences, mass degeneracies of chiral partners in the hot medium are clearly demonstrated, consistent with chiral symmetry restoration. Moreover, we find that the couplings responsible for the $U(1)$ axial anomaly are enhanced upon entering the finite temperature regime. Baryonic fluctuations also provide sizable contributions to these enhancements. Finally, the fate of the topological susceptibility in the hot QC$_2$D medium is examined.

hep-ph↗
arXiv2023

Scale dependence of the Kondo interaction in the functional renormalization group formalism

Scale evolution of interactions between a Weyl fermion and a heavy magnetic impurity is calculated non-perturbatively using the functional renormalization group technique. Using an expansion around the vanishing pairing gap, we derive the flow equations for all possible quartic couplings in the system. We find that contrary to conventional perturbation theory, the usual spin-spin isotropic interaction necessarily splits into two invariant parts during the scale evolution, which are fully allowed by the $SU(2)$ spin-rotation symmetry. We also find the existence of an infrared stable interacting fixed point, which can be responsible for intermediate-coupling screening effects. The calculation scheme presented here is rather general and expected to be easily applicable to various spin-spin-like interactions in fermionic systems.

hep-ph↗
arXiv2020

Vortex confinement transitions in the modified Goldstone model

The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.

cond-mat.stat-mech↗
arXiv2019

Charged and neutral fixed points in the O(N)+O(N)-model with Abelian gauge fields

In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity, the existence of an infrared stable charged fixed point ensures that there is a parameter range where the superconducting phase transition is second order, as opposed to fluctuation-induced first order as one would infer from the Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a two-field generalization of the Abelian-Higgs model, where two N-component fields are coupled to two gauge fields and to each other, using the functional renormalization group. Focusing mostly on three dimensions, in the neutral case, this is a model for two-component Bose-Einstein condensation, and we confirm the fixed-point structure established in earlier works using different methods. The charged model is a dual theory of two-dimensional dislocation-mediated quantum melting. We find the existence of three charged fixed points for all N>2, while there are additional fixed points for N=2.

hep-th↗
arXiv2014

Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition

Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the conventional Bardeen-Cooper-Schrieffer (BCS) theory with Gorkov and Melik-Barkhudarov (GMB) correction are clarified in details in the weak coupling region by using the renormalization group flow of the fermionic four-point vertex with particle-particle and particle-hole scattering contributions. To go beyond the BCS+GMB theory, coupled FRG flow equations of the fermion self-energy and the four-point vertex are studied under an Ansatz concerning their frequency/momentum dependence. We found that the fermion self-energy turns out to be substantial even in the weak couping region, and the frequency dependence of the four-point vertex is essential to obtain the correct asymptotic-ultraviolet behavior of the flow for the self-energy. The superfluid transition temperature and the associated chemical potential are calculated in the region of negative scattering lengths.

cond-mat.quant-gas↗
arXiv2014

Functional renormalization group approach to conventional theory of superfluidity and beyond

Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the Bardeen-Cooper-Schrieffer (BCS) theory with its Gorkov and Melik-Barkhudarov (GMB) correction is made clear, and the FRG flow of the fermion self-energy is also studied to go beyond the BCS+GMB theory. The superfluid transition temperature and the associated chemical potential are calculated in the region of the negative scattering length using fermionic FRG.

cond-mat.quant-gas↗