http://inspirehep.net/record/1347138/files/arXiv:1503.00732.pdf

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

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.

/pdf/the-qcd-equation-of-state-in-background-magnetic-fields-yfvfqcuyi5.pdf

The QCD equation of state in background magnetic fields

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

Magnetic Catalysis: A Review

We present a self-consistent model for the study of the structure of a neutron star in strong magnetic fields. Starting from a microscopic Lagrangian, this model includes the effect of the magnetic field on the equation of state, the interaction of the electromagnetic field with matter (magnetisation), and anisotropies in the energy-momentum tensor, as well as general relativistic aspects. We build numerical axisymmetric stationary models and show the applicability of the approach with one example quark matter equation of state (EoS) often employed in the recent literature for studies of strongly magnetised neutron stars. For this EoS, the effect of inclusion of magnetic field dependence or the magnetisation do not increase the maximum mass significantly in contrast to what has been claimed by previous studies.

Consistent neutron star models with magnetic-field-dependent equations of state

https://www.springer.com/cda/content/document/cda_downloaddocument/9783642373046-c2.pdf?SGWID=0-0-45-1393306-p175064717

In the present work we use the mean-field approximation to investigate quark matter described by the su(3) Nambu--Jona-Lasinio (NJL) model subject to a strong magnetic field. We consider two cases: pure quark matter and quark matter in $\ensuremath{\beta}$ equilibrium possibly present in magnetars. The results are compared with the ones obtained with the su(2) version of the model. The energy per baryon of magnetized quark matter becomes more bound than nuclear matter made of iron nuclei, for $B$ around $2\ifmmode\times\else\texttimes\fi{}{10}^{19}$ G. When the su(3) NJL model is applied to stellar matter, the maximum mass configurations are always above $1.45{M}_{\ensuremath{\bigodot}}$ and may be as high as $1.86{M}_{\ensuremath{\bigodot}}$ for a central magnetic field of $5\ifmmode\times\else\texttimes\fi{}{10}^{18}$ G. These numbers are within the masses of observed neutron stars.

M. Benghi Pinto

Papers

Quark matter under strong magnetic fields in the su(3) Nambu-Jona-Lasinio Model