Finite temperature transition for 2-flavor lattice QCD at finite isospin density

We simulate 2-flavor lattice QCD at finite isospin chemical potential μI, for temperatures close to the finite temperature transition from hadronic matter to a quark-gluon plasma. The μI dependence of the transition coupling is observed and used to estimate the decrease in the transition temperature with increasing μI. These simulations are performed on an 8³×4 lattice at three different quark masses. Our estimate of the magnitude of the fluctuations of the phase of the fermion determinant at small quark-number chemical potential μ, suggest that the position of the small μ and small μI transitions should be the same for μI=2μ, and we argue that the nature of these transitions should be the same. For all μI<m_π the smoothness of these transitions and the values of the Binder cumulant B₄, indicate that these transitions are mere crossovers, and show no sign of a critical endpoint corresponding to that expected at finite μ. This suggests that this finite μ critical endpoint, if it exists, lies at μ>m_π/2 over the considered range of quark masses. For μI>m_π and a small isospin (I₃) breaking term λ, we do find evidence of a critical endpoint which would indicate that, for λ=0, there is a tricritical point on the phase boundary where the pion condensate evaporates, where this phase transition changes from second to first-order.