The QCD equation of state in background magnetic fields

G. S. Bali, F. Bruckmann, G. Endrődi, S. D. Katz, A. Schäfer

Research output: Contribution to journalArticle

94 Citations (Scopus)


Abstract: We determine the equation of state of 2+1-flavor QCD with physical quark masses, in the presence of a constant (electro)magnetic background field on the lattice. To determine the free energy at nonzero magnetic fields we develop a new method, which is based on an integral over the quark masses up to asymptotically large values where the effect of the magnetic field can be neglected. The method is compared to other approaches in the literature and found to be advantageous for the determination of the equation of state up to large magnetic fields. Thermodynamic observables including the longitudinal and transverse pressure, magnetization, energy density, entropy density and interaction measure are presented for a wide range of temperatures and magnetic fields, and provided in ancillary files. The behavior of these observables confirms our previous result that the transition temperature is reduced by the magnetic field. We calculate the magnetic susceptibility and permeability, verifying that the thermal QCD medium is paramagnetic around and above the transition temperature, while we also find evidence for weak diamagnetism at low temperatures.

Original languageEnglish
Article number177
JournalJournal of High Energy Physics
Issue number8
Publication statusPublished - Jan 1 2014


  • Lattice QCD
  • Phase Diagram of QCD
  • Quark-Gluon Plasma

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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