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The S=1 quantum antiferromagnetic chain with the Hamiltonian H= J₈ S₈^xS₈+₁^x+S₈^yS₈+₁^y+S₈^z S₈+₁^z+D (S₈^z) ^2 is studied. By developing a (path-integral-type) stochastic geometric representation and using the ideas of percolation, we find that the Haldane phase with a unique disordered ground state and a gap can be regarded as ``liquid''. The large-D phase and the N\'eel ordered phase are identified as ``gas'' and ``solid'', respectively. We introduce a new order parameter that distinguishes the Haldane phase from other disordered phases such as the large-D phase or the dimer phase.
Hal Tasaki (Mon,) studied this question.