Geodesic
Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 493-499 
N. N. Ganikhodzhaev. Exact Solution of the Ising Model on the Cayley Tree with Competing Ternary and Binary Interactions. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 493-499. http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a7/
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     author = {N. N. Ganikhodzhaev},
     title = {Exact {Solution} of the {Ising} {Model} on the {Cayley} {Tree} with {Competing} {Ternary} and {Binary} {Interactions}},
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The exact solution is found for the problem of phase transitions in the Ising model with competing ternary and binary interactions. For the pair of parameters $\theta =\theta (J)$ and $\theta _1=\theta _1(J_1)$ in the plane $(\theta _1,\theta )$, we find two critical curves such that a phase transition occurs for all pairs $(\theta _1,\theta )$ lying between the curves.

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