Limits on hadron spectrum from bulk medium properties

We bring up the fact that the bulk thermal properties of the hadron gas, as measured on the lattice, preclude a very fast rising of the number of resonance states in the QCD spectrum, as assumed by the Hagedorn hypothesis, unless a substantial repulsion between hadronic resonances is present. If the Hagedorn growth continued above masses ~1.8 GeV, then the thermodynamic functions would noticeably depart from the measured lattice values at temperatures above 140 MeV, just below the transition temperature to quark-gluon plasma.