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Quantum chromodynamics (QCD) at finite temperature (T), baryon chemicalpotential (\muB) and isospin chemical potential (\muI) is studied in the strongcoupling limit on a lattice with staggered fermions. With the use of largedimensional expansion and the mean field approximation, we derive an effectiveaction written in terms of the chiral condensate and pion condensate as afunction of T, \muB and \muI. The phase structure in the space of T and \muB iselucidated, and simple analytical formulas for the critical line of the chiralphase transition and the tricritical point are derived. The effects of a finitequark mass (m) and finite \muI on the phase diagram are discussed. We alsoinvestigate the phase structure in the space of T, \muI and m, and clarify thecorrespondence between color SU(3) QCD with finite isospin density and colorSU(2) QCD with finite baryon density. Comparisons of our results with thosefrom recent Monte Carlo lattice simulations on finite density QCD are given.Comment: 18 pages, 6 figures, revtex4; some discussions are clarified, version  to appear in Phys. Rev.

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