Lattice QCD at finite isospin density at zero and finite temperature

We simulate lattice QCD with dynamical u and d quarks at finite chemical potential, ₈, for the third component of isospin (I₃) at both zero and at finite temperature. At zero temperature there is some ₈, ₂ say, above which I₃ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict ₂=m_. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of I₃ symmetry at high temperature for ₈>₂. For ₈ sufficiently large, this finite temperature phase transition is very abrupt, suggesting that it is first order. As ₈ is decreased it appears to become second order connecting continuously with the zero temperature transition.