Magnetic susceptibility of QCD matter and its decomposition from the lattice

Bali GS, Endrödi G, Piemonte S. Magnetic susceptibility of QCD matter and its decomposition from the lattice. Journal of High Energy Physics . 2020;2020(7): 183.We determine the magnetic susceptibility of thermal QCD matter by means of first principles lattice simulations using staggered quarks with physical masses. A novel method is employed that only requires simulations at zero background field, thereby circumventing problems related to magnetic flux quantization. After a careful continuum limit extrapolation, diamagnetic behavior (negative susceptibility) is found at low temperatures and strong paramagnetism (positive susceptibility) at high temperatures. We revisit the decomposition of the magnetic susceptibility into spin- and orbital angular momentum- related contributions. The spin term - related to the normalization of the photon lightcone distribution amplitude at zero temperature - is calculated non-perturbatively and extrapolated to the continuum limit. Having access to both the full magnetic susceptibility and the spin term, we calculate the orbital angular momentum contribution for the first time. The results reveal the opposite of what might be expected based on a free fermion picture. We provide a simple parametrization of the temperature- and magnetic field-dependence of the QCD equation of state that can be used in phenomenological studies

QCD in background magnetic fields - an overview of recent lattice results

Endrödi G. QCD in background magnetic fields - an overview of recent lattice results. In: Proceedings of 9th International Workshop on Critical Point and Onset of Deconfinement — PoS(CPOD2014). Trieste, Italy: Sissa Medialab; 2015: 038

Magnetic structure of isospin-asymmetric QCD matter in neutron stars

Endrödi G. Magnetic structure of isospin-asymmetric QCD matter in neutron stars. Physical Review D. 2014;90(9): 094501.We study QCD under the influence of background magnetic fields and isospin chemical potentials using lattice simulations. This setup exhibits a sign problem which is circumvented using a Taylor expansion in the magnetic field. The ground state of the system in the pion condensation phase is found to exhibit a pronounced diamagnetic response. We elaborate on how this diamagnetism may contribute to the pressure balance in the inner core of strongly magnetized neutron stars. In addition we show that the onset of pion condensation shifts to larger chemical potentials due to the enhancement of the charged pion mass for growing magnetic fields. Finally, we summarize the magnetic nature of QCD matter on the temperature-isospin chemical potential phase diagram

The nature of the finite temperature QCD transition as a function of the quark masses

Endrödi G. The nature of the finite temperature QCD transition as a function of the quark masses. In: Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007). Trieste, Italy: Sissa Medialab; 2008: 182

Multidimensional spline integration of scattered data

Endrödi G. Multidimensional spline integration of scattered data. Computer Physics Communications. 2011;182(6):1307-1314.We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing the deviation between its derivatives and the measured gradient. Unlike a multidimensional integration along some path, the present method results in a continuous, smooth surface, furthermore, it also applies to input data that are non-equidistant and not aligned on a rectangular grid. Function values, first and second derivatives and integrals are easy to calculate. The proper estimation of the statistical and systematical errors is also incorporated in the method

Thermal QCD with external imaginary electric fields on the lattice

Endrödi G, Marko G. Thermal QCD with external imaginary electric fields on the lattice. arXiv:2110.12189. 2021.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

Magnetic susceptibility of the QCD condensate at zero and at finite temperature from the lattice

Endrödi G. Magnetic susceptibility of the QCD condensate at zero and at finite temperature from the lattice. In: Proceedings of Xth Quark Confinement and the Hadron Spectrum — PoS(Confinement X). Trieste, Italy: Sissa Medialab; 2013: 198

QCD phase diagram: overview of recent lattice results

Endrödi G. QCD phase diagram: overview of recent lattice results. Journal of Physics: Conference Series. 2014;503: 012009.Two parameters that have a strong influence on the finite temperature QCD transition, and play an important role in various physical scenarios are the quark density and the external magnetic field. The effect of these parameters on the thermal properties of QCD is discussed, and an overview of the latest lattice results is given