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.
Highlights
The EoS gives the equilibrium description of QCD matter, in terms of relations between thermodynamic observables like the pressure, the energy density or the entropy density
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
External magnetic fields play an important role in the evolution of the early universe [7], in strongly magnetized neutron stars [8] and in non-central heavy-ion collisions, see, e.g., the recent review [9]
Summary
The fundamental quantity of thermodynamics is the free energy or thermodynamic potential. Note that the appropriate scheme to be used depends on the physical situation that one would like to describe It is specified by the trajectory B(Li), along which the compression perpendicular to the magnetic field proceeds. The pressure components for a general B(Li) trajectory (“general scheme”) can be found by combining our results for the longitudinal pressure and for the magnetization (both are contained in online resources on the paper’s page), p(xgeneral) pz. This relation reproduces the B- and Φ-schemes, eq (2.4), for the trajectories B(Li) = B and eB(Li) = Φ/(LxLy), respectively. The derivative of the magnetization with respect to B at vanishing magnetic field gives the magnetic susceptibility,
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