Amorphously packed, frustrated hierarchical models: Chaotic rescaling and spin‐glass behavior

Hierarchical Ising models have been constructed with competing ferromagnetic and antiferromagnetic interactions, and solved exactly. As frustration is increased, a low‐temperature phase is encountered, characterized by chaotic renormalization‐group trajectories. This spin‐glass phase is microscopically described in terms of subsets of spins which are strongly correlated, yet noncontiguous. Further, the amorphous packing of real systems is approximated in these models by a random distribution of shapes at various hierarchical levels, which eliminates unphysical limit cycle behavior in favor of chaos.