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Exact solution of the Ising model on the Cayley tree with competing ternary and binary interactions. (English. Russian original) Zbl 1031.82012
Theor. Math. Phys. 130, No. 3, 419-424 (2002); translation from Teor. Mat. Fiz. 130, No. 3, 493-499 (2002).
Summary: 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.

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B23 Exactly solvable models; Bethe ansatz
82B26 Phase transitions (general) in equilibrium statistical mechanics
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