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We have performed a variety of numerical studies on the general bilinear‐biquadratic spin‐1 Hamiltonian H/J=∑ N i=1[S i ⋅S i+1 −β(S i ⋅S i+1)2], over the range 0≤β≤∞. The model is Bethe Ansatz integrable at the special point β=1, where the spectrum is gapless, but is otherwise believed to be nonintegrable. Affleck has predicted that an excitation gap opens up linearly in the vicinity of β=1. Our studies involving spectral excitations (dispersion spectra), scaled‐gap, and finite‐size scaling calculations are not consistent with the Affleck prediction. The situation appears complex, with novel crossover effects occurring in both regimes, ββ>1, complicating the analysis.
J. C. Bonner, J. B. Parkinson, J. Oitmaa and H. W. J. Blöte. Unusual critical behavior in a bilinear‐biquadratic exchange Hamiltonian. J. Appl. Phys. 61 (1987), 4432.
Available at: http://dx.doi.org/10.1063/1.338400