Abstract
A recent study of second-neighbour effects in uniform magnetic chains is extended to dimerised antiferromagnetic chains. This is the first time that the Jordan-Wigner transformation has been applied to the NNN dimerised chain. The resulting Hamiltonian is then treated in the thermal Hartree-Fock approximation, yielding a distortion of the mirror symmetric bands found in the NN case. While the formalism is developed for the XY-Ising model, a detailed application is made for the Heisenberg case with weak NNN exchange interactions. Elastic (phonon) contributions to the free energy of the dimerised system are made by following the Beni-Pincus approach in order to study the spin-Peierls transition. The authors find a limiting value of the spin-phonon coupling constant ( lambda ) such that for lambda 0.611, it increases with -G. A comparison is made with the results of an alternate approach using the NNN XY uniform chain and XY spin-phonon interactions according to Pytte (1974).
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