Quantum phase transitions play a key role in the understanding the phenomena of many-body systems, especially in anti-ferromagnetic magnetic plateaus. By means of variation mean-field-like treatment based on the Gibbs–Bogoliubov inequality, it is presented the frustrated magnetization plateau and thermal concurrence properties in spin-1/2 Ising–Heisenberg models on a triangulated Kagom´e lattice and a diamond chain. Using the transfer matrix method, an exact solution for the magnetization plateau and thermal entanglement of Ising-XYZ, Blume-Emery-Griffiths and Hubbard-Ising models on a diamond chain can be obtained. Partition function zeros of the spin-1/2 and spin-1 Ising-Heisenberg models on a diamond chain have been calculated using the transfer matrix method. The existence usual and triple Yang-Lee edge singularity exponents are shown.
