ISING MODELS WITH SPIN 1

Ostap Baran

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine
Spin-1 Ising model with higher-degree spin terms (of an exchange as well as of a non-exchange origin) in the Hamiltonian is one of the most extensively studied models in condensed matter physics. That is so not only because of the fundamental theoretical interest arising from the richness of the phase diagram that is exhibited due to competition of interactions, but also because versions and extensions of this model can be applied for the description of simple and multi-component fluids [1–3], dipolar and quadrupolar orderings in magnets [3–5], crystals with ferromagnetic impurities [3], ordering in semiconducting alloys [6], etc.
Ising model with S=1 has been investigated by different simulation and approximate techniques: using the mean-field approximation [1–4, 7], effective field theory [8, 9], two-particle cluster approximation [10, 11], Bethe approximation [12], high-temperature series expansions [13], renormalization-group theory [14, 15], and Monte-Carlo simulations [12, 16, 17].
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