Effect of the entropy contribution to the free energy of strongly correlated systems in the dynamic mean-field theory of phase transitions

Conditions, under which the entropy contribution to the free energy calculated in the dynamic mean-field theory should be taken into account for the correct description of phase transitions in strongly correlated systems, have been studied using the example of the single-band Hubbard model. It has been shown that the temperature dependence of the difference between the internal and free energies of an insulator in the case of half filling differs considerably from that of a correlated metal at low temperatures and is nearly the same at high temperatures. This indicates the importance of taking into account the entropy in the description of metal-insulator phase transitions under pressure in the low-temperature region. The numerical stability of calculations of the temperature dependence of the entropy obtained by integrating over the coupling constant and by integrating the heat capacity-to-temperature ratio has been investigated.