arXiv subjects

Gergely Endrodi

Publications and source records attributed to Gergely Endrodi.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics of magnetized matter in hot and dense QCD

This chapter, to appear in the section on QCD under extreme conditions within the Encyclopedia of Nuclear Physics, aims to provide a pedagogical introduction to the physics of quarks and gluons in the presence of high temperature, nonzero (isospin) density and strong background electromagnetic fields. Extreme conditions of these types are relevant for the description of high-energy heavy-ion collisions, neutron stars and their mergers, as well as the evolution of the early Universe in its first microsecond. Most of the existing results on this topic have been obtained by means of first-principles simulations of the discretized theory of the strong interactions, lattice Quantum Chromodynamics (QCD). This lays the focus of this review chapter, although various calculations within effective theories of QCD -- most notably chiral perturbation theory -- are also discussed. Furthermore, we provide an outlook concerning open questions and yet uncharted parameter regions within this fascinating system.

hep-lat↗

arXiv2026

Exact center symmetry and first-order phase transition in QCD with three degenerate dynamical quarks

We study QCD with three degenerate flavors of dynamical quarks using first-principles lattice simulations. For a specific choice of imaginary isospin chemical potential, this theory possesses an exact center symmetry, just like pure gauge theory. This exact symmetry is expected to be intact at low temperatures and spontaneously broken in the high-temperature regime. By analyzing the finite-size scaling of the Polyakov loop distribution, obtained with a dedicated multi-histogram approach, we demonstrate that there is a first-order deconfinement phase transition in between. Our results are obtained employing stout-smeared rooted staggered quarks at one lattice spacing. Using simulations at different quark masses we sketch the behavior of QCD in the mass-isospin chemical potential plane, shedding new light on this corner of the fundamental phase diagram of the strong interactions and the relationship between chiral symmetry breaking and deconfinement.

hep-lat↗

arXiv2025

Renormalization group invariant mean-field model for QCD at finite isospin density

QCD at nonzero isospin chemical potentials has phenomenological relevance for a series of physical systems and provides an ideal testground for the modeling of dense strongly interacting matter. The two-flavor quark-meson model is known to effectively describe the condensation of charged pions in QCD that occurs in this setting. In this paper, we derive a renormalization-group invariant mean-field formulation of the model and demonstrate that the resulting phase diagram and equation of state are in quantitative agreement with data from lattice QCD simulations at small and intermediate isospin chemical potentials. In particular, the speed of sound from the model shows an excess over the conformal bound as previously seen in lattice computations in agreement with chiral perturbation theory. We then consider the speed of sound in the limit of large isospin chemical potentials and see that it approaches the conformal limit from above, in qualitative agreement with recent lattice results and in quantitative agreement with perturbation theory in the presence of a BCS gap. Finally, we consider the phase diagram in the approach to the chiral limit. We find that within the model the chiral phase transition connects to the pion condensation phase boundary in the chiral limit and we discuss the implications for the properties of the chiral transition point.

hep-ph↗

arXiv2025

First-order phase transition in dynamical 3-flavor QCD at imaginary isospin

We revisit QCD with three mass-degenerate quark flavors at an imaginary isospin chemical potential set to 4 pi T/3. This choice corresponds to a special point in the parameter space, where the theory possesses an exact Z(3) center symmetry. Through a finite-size scaling analysis, we demonstrate that in this case the finite temperature QCD transition is of first order and entails singular behavior both in the Polyakov loop and in the quark condensate. Our results are based on simulations with stout-smeared staggered quarks and a dedicated multi-histogram analysis.

hep-lat↗

arXiv2024

Equation of state of isospin asymmetric QCD with small baryon chemical potentials

We extend our measurement of the equation of state of isospin asymmetric QCD to small baryon and strangeness chemical potentials, using the leading order Taylor expansion coefficients computed directly at non-zero isospin chemical potentials. Extrapolating the fully connected contributions to vanishing pion sources is particularly challenging, which we overcome by using information from isospin chemical potential derivatives evaluated numerically. Using the Taylor coefficients, we present, amongst others, first results for the equation of state along the electric charge chemical potential axis, which is potentially of relevance for the evolution of the early Universe at large lepton flavour asymmetries.

hep-ph↗

arXiv2024

QCD with background electromagnetic fields on the lattice: a review

This review provides a comprehensive summary of results on the physics of strongly interacting matter in the presence of background electromagnetic fields, obtained via numerical lattice simulations of the underlying theory, Quantum Chromodynamics (QCD). Lattice QCD has guided our understanding of magnetized quarks and gluons via landmark results on the phase diagram, the equation of state, the confinemenent mechanism, anomalous transport phenomena as well as many more fascinating effects. Some of the lattice results lead to completely new paradigms in the description of hot magnetized quark matter and provided useful insights to a broad high-energy particle physics community. Since the first lattice QCD simulations with background fields, this field has been established as an independent research direction. We present the current status and recent developments of this field, together with an outlook including open questions to be answered in the near future.

hep-lat↗

arXiv2023

QCD phase diagram and equation of state in background electric fields

The phase diagram and the equation of state of QCD is investigated in the presence of weak background electric fields by means of continuum extrapolated lattice simulations. The complex action problem at nonzero electric field is circumvented by a novel Taylor expansion, enabling the determination of the linear response of the thermal QCD medium to constant electric fields -- in contrast to simulations at imaginary electric fields, which, as we demonstrate, involve an infrared singularity. Besides the electric susceptibility of QCD matter, we determine the dependence of the Polyakov loop on the field strength to leading order. Our results indicate a plasma-type behavior with a negative susceptibility at all temperatures, as well as an increase in the transition temperature as the electric field grows.

hep-lat↗

arXiv2023

Equation of state and speed of sound of isospin-asymmetric QCD on the lattice

We determine the QCD equation of state at nonzero temperature in the presence of an isospin asymmetry between the light quark chemical potentials on the lattice. Our simulations employ $N_f=2+1$ flavors of dynamical staggered quarks at physical masses, using three different lattice spacings. The main results are based on a two-dimensional spline interpolation of the isospin density, from which all relevant quantities can be obtained analytically. In particular, we present results for the pressure, the interaction measure, the energy and entropy densities, as well as the speed of sound. Remarkably, the latter is found to exceed its ideal gas limit deep in the pion condensed phase, the first account of the violation of this limit in first principles QCD. Finally, we also compute the phase diagram in the temperature -- isospin density plane for the first time. The data for all observables will be useful for the benchmarking of effective theories and low-energy models of QCD and are provided in ancillary files for simple reuse.

hep-lat↗

arXiv2022

QCD thermodynamics at non-zero isospin asymmetry

We study the thermodynamic properties of QCD at nonzero isospin chemical potential using improved staggered quarks at physical quark masses. In particular, we discuss the determination of the equation of state at zero and nonzero temperatures and show results. Using the results for the isospin density $n_I$, we also determine the phase diagram in the $(n_I,T)$-plane.

hep-lat↗

arXiv2021

Thermal QCD with external imaginary electric fields on the lattice

We study QCD at finite temperature in the presence of imaginary electric fields. In particular, we determine the electric susceptibility, the leading coefficient in the expansion of the QCD pressure in the imaginary field. Unlike for magnetic fields, at nonzero temperature this coefficient requires a non-trivial separation of genuine electric field-related effects and spurious effects related to the chemical potential, which becomes an unphysical gauge parameter in this setting. Our results are based on lattice simulations with stout improved dynamical staggered quarks at physical quark masses.

hep-lat↗

arXiv2019

Exploring the QCD phase diagram via reweighting from isospin chemical potential

We investigate the QCD phase diagram for small values of baryon and strange quark chemical potentials from simulations at non-zero isospin chemical potential. Simulations at pure isospin chemical potential are not hindered by the sign problem and pion condensation can be observed for sufficiently large isospin chemical potentials. We study how the related phase boundary evolves with baryonic and strange chemical potentials via reweighting in quark chemical potentials and discuss our results. Furthermore, we propose and implement an alternative method to approach nonzero baryon (and strange quark) chemical potentials. This method involves simulations where physical quarks are paired with auxiliary quarks in unphysical "isospin" doublets and a decoupling of the auxiliary quarks by mass reweighting.

hep-lat↗

arXiv2019

Magnetic catalysis and inverse catalysis for heavy pions

We investigate the QCD phase diagram for nonzero background magnetic fields using first-principles lattice simulations. At the physical point (in terms of quark masses), the thermodynamics of this system is controlled by two opposing effects: magnetic catalysis (enhancement of the quark condensate) at low temperature and inverse magnetic catalysis (reduction of the condensate) in the transition region. While the former is known to be robust and independent of the details of the interactions, inverse catalysis arises as a result of a delicate competition, effective only for light quarks. By performing simulations at different quark masses, we determine the pion mass above which inverse catalysis does not take place in the transition region anymore. Even for pions heavier than this limiting value - where the quark condensate undergoes magnetic catalysis - our results are consistent with the notion that the transition temperature is reduced by the magnetic field. These findings will be useful to guide low-energy models and effective theories of QCD.

hep-lat↗

arXiv2018

New class of compact stars: Pion stars

We investigate the viability of a new type of compact star whose main constituent is a Bose-Einstein condensate of charged pions. Several different setups are considered, where a gas of charged leptons and neutrinos is also present. The pionic equation of state is obtained from lattice QCD simulations in the presence of an isospin chemical potential, and requires no modeling of the nuclear force. The gravitationally bound configurations of these systems are found by solving the Tolman-Oppenheimer-Volkov equations. We discuss weak decays within the pion condensed phase and elaborate on the generation mechanism of such objects.

hep-ph↗

arXiv2018

QCD at nonzero isospin asymmetry

We study the phase diagram and the thermodynamic properties of QCD at nonzero isospin asymmetry at physical quark masses with staggered quarks. In particular, continuum results for the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition are presented. Our findings indicate that the pion condensation phase is restricted to $T\lesssim170$~MeV for isospin chemical potentials up to 325~MeV. We also use the data to test the range of validity of the Taylor expansion method and show first results for the equation of state.

hep-lat↗

arXiv2018

Reliability of Taylor expansions in QCD

We investigate the reliability of the Taylor expansion method in QCD with isospin chemical potentials using lattice simulations. By comparing the expansion of the number density to direct results, the range of validity of the leading- and next-to-leading order expansions is determined. We also elaborate on the convergence properties of the Taylor series by comparing the leading estimate for the radius of convergence to the position of the nearest singularity, i.e. the onset of pion condensation. Our results provide a handle for quantifying the uncertainties of Taylor expansions in baryon chemical potentials.

hep-lat↗

arXiv2018

Chiral transition via the Banks-Casher relation

We investigate the properties of the finite-temperature QCD transition towards the chiral limit using staggered quarks. Starting from the 2+1-flavor physical point, the limit of massless quarks is approached along two different trajectories in the Columbia-plot. Unlike in previous approaches, the chiral condensate is determined via the Banks-Casher relation. The first results of our finite size scaling analysis are presented.

hep-lat↗

arXiv2018

Universal magnetoresponse in QCD and $\mathcal{N}=4$ SYM

Using recent lattice data on the thermodynamics of QCD in the presence of a background magnetic field, we show that the ratio of transverse to longitudinal pressure exhibits, to good accuracy, a simple scaling behavior over a wide range of temperature and magnetic field, essentially depending only on the ratio $T/\sqrt B$. We compare this QCD response to the corresponding magnetoresponse in maximally supersymmetric Yang Mills theory. Given suitable calibrations defining the comparison, we find excellent agreement. This may be viewed as a further test of the applicability of holographic models for hot QCD.

hep-th↗

arXiv2018

Weak decay of magnetized pions

The leptonic decay of charged pions is investigated in the presence of background magnetic fields. In this situation Lorentz symmetry is broken and new fundamental decay constants need to be introduced, associated with the decay via the vector part of the electroweak current. We calculate the magnetic field-dependence of both the usual and a new decay constant non-perturbatively on the lattice. We employ both Wilson and staggered quarks and extrapolate the results to the continuum limit. With this non-perturbative input we calculate the tree-level electroweak amplitude for the full decay rate in strong magnetic fields. We find that the muonic decay of the charged pion is enhanced drastically by the magnetic field. We comment on possible astrophysical implications.

hep-lat↗