  We present numerical and analytical results for the thermodynamical
properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic
field. Special emphasis is placed on logarithmic corrections in the
susceptibility and specific heat at very low temperatures ($T/J=10^{-24}$) and
small fields. A longstanding controversy about the specific heat is resolved.
At zero temperature the spin-Peierls exponent is calculated in dependence on
the external magnetic field. This describes the energy response of the system
to commensurate and incommensurate modulations of the lattice. The exponent for
the spin gap in the incommensurate phase is given.

Statistical Mechanics