  The thermodynamic properties of a spin S=1/2 tetrameric Heisenberg
antiferromagnetic chain with alternating interactions AF1-AF2-AF1-F (AF and F
denote the antiferromagnetic and ferromagnetic couplings, respectively) are
studied by means of the transfer-matrix renormalization group method and
Jordan-Wigner transformation. It is found that in the absence of magnetic
field, the thermodynamic behaviors are closely related to the gapped low-lying
excitations, and a novel structure with three peaks in the temperature
dependence of specific heat is unveiled. In a magnetic field, a phase diagram
in the temperature-field plane for the couplings satisfying JAF1=JAF2=JF is
obtained, in which various phases are identified. The temperature dependence of
thermodynamic quantities including the magnetization, susceptibility and
specific heat are studied to characterize the corresponding phases. It is
disclosed that the magnetization has a crossover behavior at low temperature in
the Luttinger liquid phase, which is shown falling into the same class as that
in the S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors
alter at a certain field, which results from the crossing of two excitation
spectra. By means of the fermion mapping, it is uncovered that the system has
four spectra from fermion and hole excitations that are responsible for the
observed thermodynamic behaviors.
