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Since real materials may not realize the ideal Heisenberg model, more
general spin Hamiltonians have been investigated, mainly with
numerical simulations [65,66,67,68].
From these works, a phase diagram has been obtained for the
Hamiltonian with the XXZtype interaction and a uniaxial single ion
anisotropy D:
The phase diagram is shown in Fig.36 [68].
It has been found that the Haldane phase (H) exist in a relatively large
parameter region, which includes the pure Heisenberg model ().
Figure:
Phase diagram of the Hamiltonian eq.42 is shown
(cite from [68]). The symbols are: (H) Haldane phase,
(N) Néel ordered phase, (XY) XY phase, (F) Ferromagnetic phase
and (D) largeD phase.

The effect of the interchain interactions has also been
investigated [69,70,71].
Fig.37 shows the phase diagram [71] obtained from
a numerical simulation of the Hamiltonian:
where (i,j) denotes the nearest interchain neighboring pair.
It has been found that the Haldane phase (H) survives in the
presence of the interchain interaction (J'), if the single ion anisotropy (D)
is small.
Figure:
Phase diagram of the Hamiltonian (eq.43) is shown
(cite from [71]). The symbols are: (H) Haldane phase,
(N) Néel ordered phase, (XY) XY phase, and (D) largeD phase.

The above introduced theoretical works all supported Haldane's
conjecture. The next section introduces previous experimental results
of several S=1 spin systems, which were studied to test Haldane's conjecture in real
materials.
Next: 5.1.4 Experimental evidence for
Up: 5.1 Introduction
Previous: 5.1.2 The ValenceBondSolid Hamiltonian