Phase structures of strong coupling lattice QCD with finite baryon and isospin density

Quantum chromodynamics (QCD) at finite temperature $\mathrm{}\left(T\right),$ baryon chemical potential $\left({\mu }_{\mathrm{B}}\right),$ and isospin chemical potential $\left({\mu }_{\mathrm{I}}\right)$ is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, ${\mu }_{\mathrm{B}},$ and ${\mu }_{\mathrm{I}}.$ The phase structure in the space of T and ${\mu }_{\mathrm{B}}$ is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite ${\mu }_{\mathrm{I}}$ on the phase diagram are discussed. We also investigate the phase structure in the space of T, ${\mu }_{\mathrm{I}},$ and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.