Isotropic Heisenberg model

For a two-qubit isotropic Heisenberg model, there exists thermal entanglement for the antiferromagnetic case and no thermal entanglement for the... 

If b = 0, a = 1 the Ising model, if b = 1, a = 1 the isotropic Heisenberg model, and if b = 1, a = 0, the planar Heisenberg model or X-Y model is valid. In the following, the values of the exchange constants were calculated, or recalculated assuming a spin Hamiltonian of this form, instead of = - J 2 SjSi, occasionally used by certain au-... 

However, magnetic coupling behavior may be more complex to model than possible with a simple isotropic Heisenberg Spin Hamiltonian as defined in Eq. (79) and several recent studies set out to improve this description by modification of this Hamiltonian (86-89). 

The coefficients a and b (see Table 3.2) take into account the restrictions in spin dimensionality. For a = b= 1, the Heisenberg model with isotropic exchange interaction and isotropic susceptibility results. The combination of a = 1 and b = 0 yields the strictly anisotropic Ising model, in which the orientation of the spins is restricted to the z-axis. Consequently, the susceptibility is strongly orientation dependent and one needs to differentiate between x" in the direction of the z-axis ( easy axis ) and x perpendicular to z. The molar susceptibilities are then related as... 

In conttast, a Heisenberg model will be chosen in the case of highly isotropic ions such as Fe3+, Mn2+, Cr3+, Gd3+ and Ni2+. 

Table 5 Spin levels (Ei,i = 1 ), /T (in cm. K/mol) values at (in °K) corresponding to maximum anisotropy of the main values of the susceptibility /ii(ii = xx, yy, zz) tensor, /avr[Xav = (l/3)(Xxx + Xyy + Xzz)] and anisotropic D12 and A12 tensor parameters of a Fe -CN-Cu" model complex with and without trigonal Jahn-TeUer distortions from model calculations accounting for the difference of Je and Jb2 exchange coupling parameters (exchange anisotropy) or alternatively, assuming an isotropic Heisenberg exchange (1 = 1e = 1b2)...

Apart from the isotropic Heisenberg Hamiltonian Eq. (49), a very anisotropic form of interaction called the Ising model,... 

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