Fig. 1. Schematic diagrams of three physical circumstances that have very strong magnetic fields(a) Heavy ion collisions, (b) Magnetars, (c) The early Universe

Fig. 2. (a) Results of restricted lattice QCD simulations, When eB≤1GeV2, the red and blue bands stand for the chiral transitions of light (u,d) and strange quarks, respectively. AteB=3.25GeV2, the red and blue points correspond to chiral transition of light (u,d) and strange quarks, respectively, and the green points corresponds to the (de)confinement transition. Here, the dashed and dotted lines are interpolated from the above data. (b) The combined results of the restricted lattice QCD simulations for a smaller magnetic field and the anisotropic pure lattice gauge simulations at a larger magnetic field (grey region)^[41]. In these figures, the solid line stands for the first-order transition, while the rest of theline stands for crossover.

Fig. 3. QCD E-B phase diagram predicted by the two-flavor Nambu Jona-Lasinio (NJL) model with a parallel electromagnetic field. The blue, black, and red lines stand for the transitions between the phases of chiral symmetry breaking (χSB), homogeneous chiral symmetry restoration (χSR), and chiral symmetry restoration with vortices (χSRV). Here, the solid and dashed lines represent the first-order transition and crossover, respectively, while the orange point represents the critical end point.

Fig. 4. QCD μB-B phase diagram, in the chiral limit, predicted by the two-flavor Nambu Jona-Lasinio (NJL) model. The blue, black, and red lines represent the transitions between the phases of chiral symmetry breaking (χSB), chiral density wave (CDW), and homogeneous color superconductivity (2SC). Each of the transitions are first-order transitions (as represented by the solid lines). The orange point is the tricritical point in the phase diagram.

Fig. 5. QCD μI-B phase diagram predicted by the two-flavor Nambu Jona-Lasinio (NJL) model. The black and red lines represent the transitions between the phases of chiral symmetry breaking (χSB),π-superfluidity with magnetic vortices (πSFV), and homogeneousπ-superfluidity (πSF). The second-order transitions are represented by the dashed lines. The orange point is the critical point in the phase diagram.

Fig. 6. QCD Ω-B phase diagram predicted by the two-flavor Nambu Jona-Lasinio (NJL) model. The blue, black, and red lines represent the transitions between the phases of chiral symmetry breaking (χSB),π-superfluidity with magnetic vortices (πSFV), andρ-superconductivity with magnetic vortices (ρSCV). First-order and second-order transitions are represented by solid and dashed lines, respectively. The orange point is the critical point in the phase diagram