First-order transitions and triple point on a random p-spin interaction model

The effects of competing quadrupolar- and spin-glass orderings are investigated on a spin-1 Ising model with infinite-range random $p$-spin interactions. The model is studied through the replica approach and a phase diagram is obtained in the limit $p\to \mathrm{\infty }$. The phase diagram, obtained within replica-symmetry breaking, exhibits a very unusual feature in magnetic models: three first-order transition lines meeting at a commom triple point, where all phases of the model coexist.