2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95496In the present paper the Ising model with competing binary $J$ and $J_1$ interactions with spin values $\pm 1$, on a Cayley tree is considered. We study translation-invatiant Gibbs measures and corresponding free energies ones.12 pages. submittedMathematical Physics82B20On some remarks on the Ising model with competing interactions on a Cayley treetext