Partition function zeros and magnetization plateaus of the spin-1 Ising–Heisenberg diamond chain

• We consider the spin-1 Ising–Heisenberg model on a diamond chain.
• Exact ground-state phase diagrams are derived.
• The existence of the magnetic and quadrupole moments plateaus is shown.
• Distributions of the Yang–Lee and Fisher zeros have been studied.

We study the properties of the generalized spin-1 Ising–Heisenberg model on a diamond chain, which can be considered as a theoretical model for the homometallic magnetic complex [Ni3(C4H2O4)2−(μ3−OH)2(H2O)4]n⋅(2H2O)n. The model possesses a large variety of ground-state phases due to the presence of biquadratic and single-ion anisotropy parameters. Magnetization and quadrupole moment plateaus are observed at one- and two-thirds of the saturation value. The distributions of Yang–Lee and Fisher zeros are studied numerically for a variety of values of the model parameters. The usual value σ=−12 alongside an unusual value σ=−23 ​is determined for the Yang–Lee edge singularity exponents.