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Lattice QCD at finite isospin chemical potential and temperature

We simulate lattice QCD at a finite chemical potential $μ_I$ for isospin ($I_3$) at zero and finite temperatures. At some $μ_I=μ_c$ QCD has a second order transition with mean-field critical exponents to a state where ($I_3$) is broken spontaneously by a charged pion condensate. Heating the system with $μ_I > μ_c$ we find there is some temperature at which this condensate evaporates. This transition appears to be second order and mean-field at lower $μ_I$ values, and first order for $μ_I$ sufficiently large. We are determining the dependence of the finite temperature crossover $T_c$ on $μ_I$ for $μ_I < μ_c$. This is expected to be identical to $T_c$'s dependence on quark-number chemical potential $μ_q$ for small $μ_q$.