By Selvitella A.
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Extra resources for Asymptotic evolution for the semiclassical nonlinear Schrodinger equation in presence of electric and magnetic fields
Experimental and theoretical magnetic behavior of MnCo(EDTA) · 6H2 O. 6 K). A comparison with uniform chain (– – –) and dimer (– · – · –) limits is shown in the inset [49,81]. (T < 30 K). 22 (Fig. 20). It is worth underlining the simplicity and the flexibility of this model, which also allows the introduction of a z-axial anisotropy. A detailed discussion of local uniaxial anisotropy effects has been done for the [1–1] Ising chain, which involves (3 × 3) transfer matrices. Such a system needs a mathematical treatment through the socalled Cardan method for finding the roots of a third-degree polynomial .
In spite of its two-sublattice structure, the magnetic behavior of this compound does not exhibit any χ T divergence in the low temperature range (Fig. 21). The compensation problem (for purely AF coupling) has already been mentioned in connection with both quantum and classical isotropic models. In the classical context, it has been pointed out that the low-temperature behavior results from a subtle conflict between the short-range ordering, which reduces the effective moment carried by a pair of consecutive spins, and the long-range one, which assembles these spins into quasi-rigid fragments.
The author solved the random problem for spin–spin correlations, using Eq. (9) i. 3 Classical-spin Heisenberg Chains 15 tions ui+m · ui+m+1 (m = 0, 1, . . , j − 1). The wave-number-dependent magnetic cross-section S(q) was deduced, but the corresponding magnetic susceptibility χ0 (q) was not given. However it can be easily related to the spin–spin correlation functions in random as well as in regular systems. In this context it can be useful to mention the fragment chain model, which corresponds to a special random chain in which one of the species is nonmagnetic .
Asymptotic evolution for the semiclassical nonlinear Schrodinger equation in presence of electric and magnetic fields by Selvitella A.