PACS. 05.50.+q -Lattice theory and statistics: Ising problem. PACS. 05.70.Fh -Phase transitions: general aspects. PACS. 64.60.Cn -Order-disorder and statistical mechanics of model systems. AbstractThe spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed and full set of phase diagrams are constructed for both positive and negative biquadratic couplings. A comparison with the results of other approximation schemes is done. *

The antiferromagnetic Ising model in a magnetic field is considered on the Husimi tree. Using iteration technique we draw the plots of magnetization versus external field for different temperatures and construct the resulting phase diagram. We show that frustration effects essentially change the critical properties. The model exhibits three distinct critical regions, including re-entrant phase structure and Griffiths

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