Chiral nuclear thermodynamics

We calculate the equation of state of nuclear matter for arbitrary isospin-asymmetry up to three loop order in the free energy density in the framework of in-medium chiral perturbation theory. In our approach 1\pi- and 2\pi-exchange dynamics with the inclusion of the \Delta-isobar excitation as an explicit degree of freedom, corresponding to the long- and intermediate-range correlations, are treated explicitly. Few contact terms fixed to reproduce selected known properties of nuclear matter encode the short-distance physics. Two-body as well as three-body forces are systematically included. We find a critical temperature of about 15 MeV for symmetric nuclear matter. We investigate the dependence of the liquid-gas first-order phase transition on isospin-asymmetry. In the same chiral framework we calculate the chiral condensate of isospin-symmetric nuclear matter at finite temperatures. The contribution of the \Delta-isobar excitation is essential for stabilizing the condensate. As a result, we find no indication of a chiral phase transition for densities \rho \lesssim 2 \rho_0 and at temperatures T \lesssim 100 MeV.