  In QCD with two massless quarks, the chiral phase transition is plausibly in
the same universality class as the classical O(4) magnet. To test this
hypothesis, critical exponents characterizing the behaviour of universal
quantities near the 2nd order critical point can be calculated and compared to
results from lattice simulations. Present simulations already allow many
qualitative tests; quantitative tests await future simulations with longer
correlation lengths. In a heavy ion collision, a long correlation length would
lead to large fluctuations in the number ratio of neutral to charged pions.
Unfortunately, no equilibrium correlation length gets long enough for this to
occur. Modelling the dynamics of the chiral order parameter in a far from
equilibrium transition by quenching in the linear sigma model suggests that
long wavelength modes of the pion field can be amplified. This could have
dramatic phenomenological consequences. Theoretical advances include attempts
to relax the quench approximation and to include expansion and quantum effects.
Long wavelength pion oscillations arise in a number of theoretical treatments;
however, all involve idealizations and are at best qualitative guides. It is up
to experimentalists to determine whether such phenomena occur; detection in a
heavy ion collision would imply an out of equilibrium chiral transition.
