Heisenberg systems

There are essential differences between the systems we have presented here, even in the limit of very strong anisotropy. The RKKY spin glasses are Heisenberg systems with random unidirectional anisotropy. Ferrofluids frozen under zero field are Heisenberg systems with random uniaxial anisotropy, while an Ising system is characterized by parallel uniaxial anisotropy. 

K is noteworthy (Allemand et al., 1991). Cgo TDAE is a soft ferromagnet and is a low-dimensional (possibly Heisenberg) system (Rao Seshadri, 1994). It does not show remnance in the magnetization curve. 

Here, a is called the alternation parameter specifying the ratio of the exchange energies, /ex and J ex = aJex. For 0 < a < 1, both exchange energies have the same sign, a = 1 results in the equidistant chain, and a = 0 describes isolated dimers. As with uniform chains, the susceptibility of such Heisenberg systems can only be approximated. 

The Hamilton-Jacobi form of the classical equations of motion has been shown to have provided the basis for the quantum-mechanical formulations according to Sommerfeld, Heisenberg, Schrodinger and Bohm. Each of these formulations inspired its own peculiar interpretation of quantum effects, despite their common basis. Each of the different points of view still has its adherents and the debates about their relative merits continue. Closer scrutiny shows that the Sommerfeld and Heisenberg systems assume quanta to be particles in the classical sense, although Heisenberg considered electronic positions to be fundamentally unobservable. 

A large number of publications have dealt with 1-D Heisenberg systems, among which the studies of Smith and Friedberg should be mentioned24). They proposed a slight modification of the Fisher curve concerning the correction for the finite spin of the studied ion (multiplication of both X and K by 4S(S + 1)). 

In contrast to the Ising model, spin-flop is observed in Heisenberg systems over a large range of applied fields and temperatures. 

In Table 11 are compiled the results concerning 2-D Heisenberg systems a is the anisotropy coefficient and the perpendicular susceptibility is calculated from the relationship ... 

By fitting the low temperature susceptibility data to a series expansion for the spin-1/2, ID Heisenberg system [49], we find a 1/T2 dependence of the susceptibility which confirms the quasi-ID behaviour and gives a ferromagnetic coupling constant of 50 K. This plot is shown in Fig. 20a. McConnell s mechanism for ferromagnetic exchange... 

Now we turn to the second question about the observation of AT-like Unes even for typical Heisenberg systems. To reconcile this result with the mean-field... 

Cu(C H2 + 1 NH3)2Cl4 They exhibit magnetic order and approximate a two-dimensional Heisenberg system. These layered materials are orthorhombic and the crystal structure is shown in Figure 22. The CUCI2 layers are separated by two layers of (C H2 + j-... 

---