Chaotic spin glasses: An upper critical dimension (invited)

The chaotic renormalization‐group trajectories exhibited by frustrated hierarchical Ising models have been interpreted as signaling a spin‐glass phase, since, as the system is probed at successive length scales, strong and weak correlations are encountered in a chaotic sequence. Cluster‐hierarchical models have been introduced, with susceptibilities behaving as in Bravais lattices. Frustrated cluster‐hierarchical models again show an ordered phase characterized by chaotic rescaling and a smooth specific heat at the transition (α<−5). Scans in dimensionality reveal an upper critical dimension for the chaotic spin‐glass phase, via a boundary crisis mechanism. Beyond this dimension, the system has no long‐range order at any temperature. Nevertheless, a low‐temperature regime can be distinctly identified, exhibiting intermediate‐range chaotic spin‐glass order.