Magnetic-field induced critical endpoint

The phase diagram of strong interaction matter is analyzed utilizing the Nambu–Jona-Lasinio model. Special emphasis is placed on its dependence on an external magnetic field and isospin chemical potential. Using flavor mixing induced by instanton effects the influence of isospin breaking due to the magnetic field and the isospin chemical potential is compared. It is found that at low temperatures and large quark chemical potential the magnetic field, depending on its strength, induces a new critical endpoint or a triple point.

Figure 1

Upper plot: Constituent quark masses $M_u$ and $M_d$ depending on the temperature for $B=0,{\mu }_q=250\mathrm{MeV}$ and ${\mu }_{\mathrm{I}}=60\mathrm{MeV}$. For comparison the result for $c=1/2$ is depicted in gray. Lower plot: Dashed crossover lines and solid first order lines for the up-quark condensate (blue) and the down-quark condensate (red) for $B=0$ and ${\mu }_{\mathrm{I}}=60\mathrm{MeV}$. For comparison the result for ${\mu }_{\mathrm{I}}=0$ is depicted in gray.

Figure 2

Dashed crossover lines and solid first order lines for the up-quark condensate (blue) and the down-quark condensate (red) for $|eB|=20m_{\pi }^2$ and ${\mu }_{\mathrm{I}}=0$. For comparison the result for $|eB|=0$ is depicted in gray.

Figure 3

Dashed crossover lines and solid first order lines for the up-quark condensate (blue) and the down-quark condensate (red) for $|eB|=20m_{\pi }^2$ and ${\mu }_{\mathrm{I}}=60\mathrm{MeV}$. For comparison the result for $|eB|=0$ and ${\mu }_{\mathrm{I}}=0$ is depicted in gray.

Figure 4

Dashed crossover lines and solid first order lines for the up-quark condensate (blue) and the down-quark condensate (red) for $|eB|=10m_{\pi }^2$ and ${\mu }_{\mathrm{I}}=0$. The new phase $C_0$ for the down quark is bounded by the solid, black first order line.

Figure 5

Left plot: Zoomed version of Fig. 4 with $|eB|=10m_{\pi }^2$. The phase $C_0$ is enclosed by the red and black first order lines. Right plot: Same plot, but with $|eB|=10.5m_{\pi }^2$. The solid, black first order line ends in a new critical endpoint.