  The exactly solvable spin-1/2 Ising-Heisenberg model on diamond chain has
been considered. We have found the exact results for the magnetization by using
recursion relation method. The existence of the magnetization plateau has been
observed at one third of the saturation magnetization in the antiferromagnetic
case. Some ground-state properties of the model are examined. At low
temperatures, the system has two ferrimagnetic (FRI1 and FRI2) phases and one
paramagnetic (PRM) phase. Lyapunov exponents for the various values of the
exchange parameters and temperatures have been analyzed. It have also been
shown that the maximal Lyapunov exponent exhibits plateau. Lyapunov exponents
exhibit different behavior for two ferrimagnetic phases. We have found the
existence of the supercritical point for the multi-dimensional rational mapping
of the spin-1/2 Ising-Heisenberg model on diamond chain for the first time at
absence of the external magnetic field and $T \rightarrow 0$ in the
antiferromagnetic case.
