Exact solution of the ising model on the cayley tree with competing ternary ad binary interactions

摘要

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 θ = θ(J) and θ_1 = θ_1(J_1) in the plane (θ_1, θ), we find two critical curves such that a phase transition occurs for all pairs (θ_1, θ) lying between the curves.