Exactly solvable spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins. 
The spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins is rigorously solved using the transfer-matrix method.  In particular, exact results for the ground state, magnetization process and specific heat are presented and discussed.  It is shown that further-neighbor interaction between nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model without this interaction term.  The zero-field specific heat displays interesting thermal dependencies with a single- or double-peak structure.