Phase Transitions in Quenched Random Mixtures on a Cactus Tree

Abstract

A phase transition in a quenched ferro- and antiferromagnetic Ising mixture on an infinite triangular Cactus tree is rigorously studied. The non-periodic ordered phase which is specified by the “phase indicator” is determined so as to exhibit the highest transition temperature. This phase is intimately associated with the ground-state spin arrangement. The critical concentration below which the magnetization should disappear at the absolute zero is also derived.