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.
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Hovhannisyan, V. V., Strečka, J., & Ananikian, N. S. (2016). Exactly solvable spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins. Journal of Physics: Condensed Matter, 28(8), . https://doi.org/10.1088/0953-8984/28/8/085401