Quenched lattice QCD at finite isospin density and related theories

We study quenched QCD at finite chemical potential ${\mu }_I$ for the third component of isospin and quenched two-color QCD at finite chemical potential $\mu$ for quark number. In contrast with the quenched approximation to QCD at finite quark-number chemical potential, the quenched approximations to these theories behave similarly to the full theories. The reason is that these theories have real positive fermion determinants. In both of these theories there is some critical chemical potential above which the charge coupled to the chemical potential is spontaneously broken. In each case, the transition appears to be second order. We study the scaling properties near the critical point using scaling functions suggested by effective (chiral) Lagrangians and find evidence for scaling with mean-field critical exponents in each case. The subtleties associated with observing the critical scaling of these theories are discussed.