  We report the exact dimer phase, in which the ground states are described by
product of singlet dimer, in the extended XYZ model by generalizing the
isotropic Majumdar-Ghosh model to the fully anisotropic region. We demonstrate
that this phase can be realized even in models when antiferromagnetic
interaction along one of the three directions. This model also supports three
different ferromagnetic (FM) phases, denoted as $x$-FM, $y$-FM and $z$-FM,
polarized along the three directions. The boundaries between the exact dimer
phase and FM phases are infinite-fold degenerate. The breaking of this
infinite-fold degeneracy by either translational symmetry breaking or
$\mathbb{Z}_2$ symmetry breaking leads to exact dimer phase and FM phases,
respectively. Moreover, the boundaries between the three FM phases are critical
with central charge $c=1$ for free fermions. We characterize the properties of
these boundaries using entanglement entropy, excitation gap, and long-range
spin-spin correlation functions. These results are relevant to a large number
of one dimensional magnets, in which anisotropy is necessary to isolate a
single chain out from the bulk material. We discuss the possible experimental
signatures in realistic materials with magnetic field along different
directions and show that the anisotropy may resolve the disagreement between
theory and experiments based on isotropic spin-spin interactions.
