  The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice is
exactly solved using a star-triangle transformation, which affords an exact
mapping correspondence to an effective spin-1/2 Ising model on a triangular
lattice. The ground-state phase diagram of both investigated quantum spin
models display two spontaneously ordered ferromagnetic phases and one
macroscopically degenerate disordered phase. In contrast to a classical
ferromagnetic phase where the spontaneous magnetization of the Ising as well as
Heisenberg spins acquire fully saturated values the spontaneous magnetization
of the Heisenberg spins is subject to a quantum reduction to one-third of its
saturated value within a quantum ferromagnetic phase. The spontaneous
magnetization and logarithmic divergence of the specific heat as the most
essential features of both ferromagnetic phases disappear whenever the
investigated quantum spin model is driven to the highly degenerate disordered
phase. The disordered phase with nonzero residual entropy originates either
from a geometric spin frustration caused by antiferromagnetic interactions or
more strikingly it may also alternatively arise from a competition of the
ferromagnetic Ising and Heisenberg interactions of easy-axis and easy-plane
type, respectively. All three available ground states coexist together at a
single triple point, around which anomalous magnetic and thermodynamic behavior
can be detected.
