Two-flavor staggered fermion thermodynamics at N-t=12

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date, approximately 0.1 fm. Of particular interest are (1) a study of the temperature of the crossover, an important indicator of continuum scaling, (2) a determination of the induced baryon charge and baryon susceptibility, used to study the dissolution of hadrons at the crossover, (3) the scalar susceptibility, a signal for the appearance of soft modes, and (4) the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for N-t = 4, 6, and 8, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature-dependent ''constituent quark free energy.''