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.