  Finite-temperature properties of weakly doped antiferromagnets as modeled by
the two-dimensional t-J model and relevant to underdoped cuprates are
investigated by numerical studies of small model systems at low doping. Two
numerical methods are used: the worldline quantum Monte Carlo method with a
loop cluster algorithm and the finite-temperature Lanczos method, yielding
consistent results. Thermodynamic quantities: specific heat, entropy and spin
susceptibility reveal a sizeable perturbation induced by holes introduced into
a magnetic insulator, as well as a pronounced temperature dependence. The
diamagnetic susceptibility introduced by coupling of the magnetic field to the
orbital current reveals an anomalous temperature dependence, changing character
from diamagnetic to paramagnetic at intermediate temperatures.
