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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     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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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/

[1] M. Mariz, C. Tsallis, E. L. Albuquerque, J. Stat. Phys., 40 (1985), 577–592 | DOI | MR

[2] C. R. da Silca, S. Coutinho, Phys. Rev. B, 34 (1986), 7975–7985 | DOI

[3] J. L. Monree, J. Stat. Phys., 67 (1992), 1185–1200 | DOI | MR

[4] J. L. Monree, Phys. Lett. A, 188 (1994), 80–84 | DOI

[5] R. Kindermann, J. L. Snell, Markov Random Fields and their Applications, Contemporary Mathematics, 1, AMS, Providence, R.I., 1980 | DOI | MR | Zbl

[6] G. Korn, T. Korn, Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1968 | MR

[7] W. Weidlich, Br. J. Math. Statist. Psychol., 24:2 (1971), 251–266 | DOI | Zbl