High-Precision Thermodynamics and Hagedorn Density of States

We compute the entropy density of the confined phase of QCD without quarks on the lattice to very high accuracy. The results are compared to the entropy density of free glueballs, where we include all the known glueball states below the two-particle threshold. We find that an excellent, parameter-free description of the entropy density between 0.7Tc and Tc is obtained by extending the spectrum with the exponential spectrum of the closed bosonic string.