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

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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. 
@article{TMF_2002_130_3_a7,
     author = {N. N. Ganikhodzhaev},
     title = {Exact {Solution} of the {Ising} {Model} on the {Cayley} {Tree} with {Competing} {Ternary} and {Binary} {Interactions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {493--499},
     publisher = {mathdoc},
     volume = {130},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a7/}
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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/