QCD thermodynamics from an imaginaryμB: Results on the four flavor lattice model

We study four flavor QCD at nonzero temperature and density by analytic continuation from an imaginary chemical potential. The explored region is $T=0.95T_c<T<3.5T_c$, and the baryochemical potentials range from 0 to $\simeq 500\mathrm{M}\mathrm{e}\mathrm{V}$. Observables include the number density, the order parameter for chiral symmetry, and the pressure, which is calculated via an integral method at fixed temperature and quark mass. The simulations are carried out on a ${16}^3\times 4$ lattice, and the mass dependence of the results is estimated by exploiting the Maxwell relations. In the hadronic region, we confirm that the results are consistent with a simple resonance hadron gas model, and we estimate the critical density by combining the results for the number density with those for the critical line. In the hot phase, above the end point of the Roberge-Weiss transition $T_E\simeq 1.1T_c$, the results are consistent with a free lattice model with a fixed effective number of flavor slightly different from four. We confirm that confinement and chiral symmetry are coincident by a further analysis of the critical line, and we discuss the interrelation between thermodynamics and critical behavior. We comment on the strength and weakness of the method, and propose further developments.