  Even though the Hubbard model is one of the most fundamental models of highly
correlated electrons, analytical and numerical data describing its
thermodynamics at nonzero magnetization are relatively scarce. We present a
detailed investigation of the thermodynamic properties for the one dimensional
repulsive Hubbard model in the presence of an arbitrary magnetic field for all
values of the filling fraction and temperatures as low as $T \sim 0.005\, t.$
Our analysis is based on the system of integral equations derived in the
quantum transfer matrix framework. We determine the critical exponents of the
quantum phase transitions and also provide analytical derivations for some of
the universal functions characterizing the thermodynamics in the vicinities of
the quantum critical points. Extensive numerical data for the specific heat,
susceptibility, compressibility, and entropy are reported. The experimentally
relevant double occupancy presents an interesting doubly nonmonotonic
temperature dependence at intermediate values of the interaction strength and
also at large repulsion and magnetic fields close to the critical value. The
susceptibility in zero magnetic field has a logarithmic singularity at low
temperatures for all filling factors similar to the behavior of the same
quantity in the XXX spin chain. We determine the density profiles for a
harmonically trapped system and show that while the total density profile seems
to depend mainly on the value of chemical potential at the center of the trap
the distribution of phases in the inhomogeneous system changes dramatically as
we increase the magnetic field.
