  Ground state and thermodynamics of geometrically frustrated spin-1/2
Ising-Heisenberg model on two different but topologically related
triangles-in-triangles lattices is investigated in particular. A rigorous
mapping based on generalized star-triangle transformations enables one to
derive exact analytical results for the free and internal energy, spontaneous
magnetization, entropy and specific heat from the known exact results for the
corresponding spin-1/2 Ising model on a triangular lattice. It is demonstrated
that several unconventional quantum ordered and disordered phases may become
the ground state in addition to the classical ferromagnetic phase with a
perfect alignment of all constituent spins. A mutual competition between the
ferromagnetic Ising and XXZ Heisenberg interactions may lead to an appearance
of a peculiar quantum ferromagnetic phase, in which the magnetic moment of the
Heisenberg spins undergoes a quantum reduction to one third of the saturation
value in contrast with the fully saturated magnetic moment of the classical
Ising spins. In the highly frustrated regime, we have found either the
disordered quantum paramagnetic phase with the substantial residual entropy or
a similar but strikingly spontaneously long-range ordered phase, in which a
quantum reduction of the magnetic moment of the Heisenberg spins causes a small
quantum reduction of the magnetic moment of otherwise purely classical Ising
spins. It is evidenced that the specific heat exhibits diverse thermal
dependences with or without a logarithmic divergence superimposed either on one
or two round Schottky-type maxima.
