Infinitely Stable Disordered Systems on Emergent Fractal Structures

TL;DR

This paper demonstrates that certain disordered systems can exhibit infinitely stable ordering at high disorder levels, with transitions localized on emergent fractal structures, challenging previous beliefs about disorder effects.

Contribution

It introduces examples of disordered systems where ordering persists infinitely and remains stable at high disorder, mediated by emergent fractal boundary structures.

Findings

Ordering exists at arbitrarily large disorder strength.

Transition temperature remains nonzero in the infinite disorder limit.

Order is localized on a boundary of a percolating fractal structure.

Abstract

In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit any finite temperature ordering. Here, we show that this is not necessarily true. We provide physically motivated examples of systems in which disorder induces an ordering that is *infinitely stable* in the sense that: (1) there exists ordering at arbitrarily large disorder strength and (2) the transition temperature remains, asymptotically, nonzero in the limit of infinite disorder. The ordering is spatially localized on the boundary of a disorder-induced, emergent percolating fractal structure. The examples we give are most naturally described when the spatial dimension $d \ge 3$, but can also be formulated when $d=2$, provided that the underlying graph is non-planar.