  The asymmetric tetrahedron is composed by all edges of tetrahedron
represented by Ising interaction except one, which has a Heisenberg type
interaction. This asymmetric tetrahedron is arranged connecting a vertex which
edges are only Ising type interaction to another vertex with same structure of
another tetrahedron. The process is replicated and this kind of lattice we call
the asymmetric Ising-Heisenberg chain. We have studied the ground state phase
diagram for this kind of models. Particularly we consider two situations in the
Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2)
Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ
chain, where we have found a rich phase diagram and a number of multicritical
points. Additionally we have also studied their thermodynamics properties and
the correlation function, using the decorated transformation. We have mapped
the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain,
and we have also concluded that it is possible to evaluate the partition
function including a longitudinal external magnetic field.
