The magnetization process, the susceptibility, and the specific heat of the spin-
1∕2 antiferromagnet (AF)-AF-ferromagnet (F) and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at
m=1∕6 for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.
The renormalization-group method is reformulated in a way that allows the analysis of two-dimensional Heisenberg ferromagnets with small spin. A set of recursion equations is derived in a one-loop approximation. The low-temperature asymptotics of the correlation length and the uniform susceptibility are obtained. The comparison of the results with the results obtained within the momentum shell recursion technique shows that even at one-loop approximation there is a sensitive renormalization due to small spin.