We present evidence for the absence of a gap in a class of S=1
antiferromagnetic exchange models. The spin exchange is long-ranged of the type
−(−1)i−j/∣i−j∣α where 1<α<3. We have shown previously that
without the alternating factor the model for α=2 (S=1 Haldane-Shastry
model) has a gap, exponentially decaying correlation functions and
exponentially small susceptibility at very low temperatures. In the case of the
alternated interaction the stabilizing next nearest neighbor ferromagnetic
interaction changes qualitatively the behavior of the system. We have studied
the groundstate and first excited state using a modified Lanczos algorithm for
system sizes up to 16 sites. Also, we performed exact diagonalization for
systems up to 8 sites and obtained the thermodynamics. The correlation
functions decay with distance like a power law. These models define a new class
of integer spin chains that do not show a Haldane gap. The results may be
relevant to describe impurity spins coupled by a RKKY-interaction through a
half-filled conduction-electron band.Comment: 19 pages, 13 figures, RevTex, improved version, to appear in Journal
of Physics: Condensed Matte