Dynamical Properties of One-Dimensional Heisenberg Model

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The dynamic properties of one-dimensional Heisenberg model have been investigated for arbitrary temperature and wave number by using the method of canonical correlation function combined with the higher random phase approximation. Among others the following two problems were in mind: (i) What is a physical background which leads the spin-wave-like excitation in the one-dimensional spin system? (ii) Are there any characteristic difference arising from the lattice dimensionality? Although there exists no long range order in one-dimensional system at finite temperature, a certain kind of short range order is developed for temperatures satisfying k_BT<J. Then one may imagine a cell-like structure with a temperature-dependent size L(T) and with a finite life time. This situation seems to be the physical background for the observation of the spin-wave-like excitation in one-dimensional system. The size for the cell-like structure is roughly estimated by the critical wave number k_c(T), i.e., L(T)≃k_c^<-1>(T) which specifies the transition of the spectral line shape from a diffusive type to an oscillatory one. In general, the magnetic properties are strongly affected by the lattice dimensionality. The magnetic behaviour of one-dimensional system has no exact correspondence to those of three-dimensional one above the transition temperature. In particular, in the lowest temperature range, the features of the one-dimensional system are in a sense closer to an ordered state in three-dimensional magnets. Computed results are compared with the experimental data on neutron inelastic scattering in (CD_3)_4NMnCl_3.
理論物理学刊行会の論文
1973-06-25

Dynamical Properties of One-Dimensional Heisenberg Model

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