  The thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets (HFM)
in an external magnetic field is investigated within a second-order two-time
Green function formalism in the wide temperature and field range. A crucial
point of the proposed scheme is a proper account of the analytical properties
for the approximate transverse commutator Green function obtained as a result
of the decoupling procedure. A good quantitative description of the correlation
functions, magnetization, susceptibility, and heat capacity of the HFM on a
chain, square and triangular lattices is found for both infinite and
finite-sized systems. The dependences of the thermodynamic functions of 2D HFM
on the cluster size are studied. The obtained results agree well with the
corresponding data found by Bethe ansatz, exact diagonalization, high
temperature series expansions, and quantum Monte Carlo simulations.
