  For the time being isotropic three-body exchange interactions are scarcely
explored and mostly used as a tool for constructing various exactly solvable
one-dimensional models, although, generally speaking, such competing terms in
generic Heisenberg spin systems can be expected to support specific quantum
effects and phases. The Heisenberg chain constructed from alternating S=1 and
sigma=1/2 site spins defines a realistic prototype model admitting extra
three-body exchange terms. Based on numerical density-matrix renormalization
group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that
the additional isotropic three-body terms stabilize a variety of
partially-polarized states as well as two specific non-magnetic states
including a critical spin-liquid phase controlled by two Gaussinal conformal
theories as well as a critical nematic-like phase characterized by dominant
quadrupolar S-spin fluctuations. Most of the established effects are related to
some specific features of the three-body interaction such as the promotion of
local collinear spin configurations and the enhanced tendency towards
nearest-neighbor clustering of the spins. It may be expected that most of the
predicted effects of the isotropic three-body interaction persist in higher
space dimensions.
