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, mu(I), for the third component of isospin (I-3) at both zero and at finite temperature. At zero temperature there is some mu(I), mu(c) say, above which I-3 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 mu(c)=m(pi). 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 I-3 symmetry at high temperature for mu(I)>mu(c). For mu(I) sufficiently large, this finite temperature phase transition is very abrupt, suggesting that it is first order. As mu(I) is decreased it appears to become second order connecting continuously with the zero temperature transition.