  We study the thermodynamics of the one-dimensional extended Hubbard model at
half-filling using a density-matrix renormalization group method applied to
transfer matrices. We show that the various phase transitions in this system
can be detected by measuring usual thermodynamic quantities like the isothermal
compressibility and the uniform magnetic susceptibility. For the isothermal
compressibility we show that universal crossing points exist which allow to
accurately determine the line where the charge gap vanishes. By studying in
addition several correlation functions, we confirm the existence of a phase
with long-range dimer order (bond order) which has been a matter of debate for
several years. According to our calculations this phase is located in a narrow
region between the spin-density and charge-density wave phases up to a
tricritical point which we estimate to be at $U_t=6.7\pm 0.2$, $V_t =3.5\pm
0.1$. Our results for the phase diagram are in good agreement with the most
recent zero-temperature density-matrix renormalization group study, however,
they disagree in some important aspects from the most recent
Quantum-Monte-Carlo study.
