Thermodynamics of the planar Hubbard model

The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility ${\ensuremath{\chi}}_{s},$ and charge susceptibility ${\ensuremath{\chi}}_{c}$ are studied as functions of temperature and doping within the two-dimensional Hubbard model with various $U/t=4\char21{}12.$ Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density $n\ensuremath{\sim}1\ifmmode\pm\else\textpm\fi{}0.15$ in the whole regime of studied $U/t.$ The pseudogap in ${\ensuremath{\chi}}_{s}(T)$ becomes clearly pronounced for $U/tg~8$ while ${\ensuremath{\chi}}_{c}$ shows a maximum close to half-filling. The relation of results to those within the $t\ensuremath{-}J$ model and to experiments is discussed.