Thermodynamic properties of the planar $t-J$ model

Several thermodynamic quantities within the planar $t-J$ model are calculated using the $T>0$ Lanczos method on clusters of up to 26 sites. Hole density $c_h(\mu,T)$ shows a non-Fermi liquid behavior as a function of $T$ and suggests a transition from small to large Fermi surface at $c_h\sim 0.15$. Specific heat reveals a maximum at the exchange energy-scale up to $c_h=0.2$, where it becomes almost $T$-independent for $T\agt 0.15~t$. At constant $T$ the entropy has maximum for $c_h\sim 0.15$, with large values at low $T$, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility $\chi_0(T)$ exhibits a maximum at finite $T = T^*$, with $T^*$ decreasing with doping, and disappearing for $c_h>0.15$.