Excitation spectrum and low-temperature thermodynamics of the Ising-Heisenberg linear ferromagnet

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Abstract
Important new analytic results have been obtained for the linear, ferromagnetic, spin-½, Ising-Heisenberg model in a small magnetic field. Specifically, for zero field an expression, which changes its form at an intermediate value of the variable anisotropy parameter, has been obtained for the thermal excitation energy gap. This special anisotropy value does not correspond to a symmetry change in the Hamiltonian, but is associated with an important difference in the physical significance of the results. For anisotropy greater than the special value, the dominant excitations correspond to bound spin complexes. For anisotropy less than the special value, the dominant excitations are spin waves. These results govern the low-temperature behavior of the specific heat. The effective magnetic excitation gap, which determines the low-temperature susceptibility, is dominated at zero field by the bound states for all anisotropy. More complex crossover effects occur in both specific heat and susceptibility when the analysis is extended to nonzero field. These results may have an important bearing on the quantum soliton problem in the linear ferromagnet.