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Low-temperature magnetic properties of both classical and quantum dimerizedferromagnetic spin chains are studied. It is shown that at low temperatures theclassical dimerized model reduces to the classical uniform model with theeffective exchange integral $J_{0}=J(1-\delta^{2})$, where $\delta$ is thedimerization parameter. The partition function and spin correlation functionare calculated by means of mapping to the continuum limit, which is justifiedat low temperatures. In the continuum limit the calculation of the partitionfunction and spin correlation function is reduced to the eigenvalue problem ofquantum rotator in gravitational field. Quantum model is studied usingDyson-Maleev representation of the spin operators. It is shown that in thelong-wavelength limit the Hamiltonian of the quantum dimerized chain reduces tothat of the uniform ferromagnetic chain with the effective exchange integral$J_{0}=J(1-\delta^{2})$. This fact implies that the known equivalence of thelow-temperature magnetic properties of classical and quantum ferromagneticchains remains for the dimerized chains. The considered model can begeneralized to include the next-neighbor antiferromagnetic interaction.

Universal low-temperature magnetic properties of the classical and quantum dimerized ferromagnetic spin chain