The Gardner transition has been studied theoretically and numerically in various models of disordered systems, such as spin glasses, structural glasses, and jammed packings. It is related to the concept of replica symmetry breaking, which describes the emergence of multiple metastable states in systems with quenched disorder. The Gardner transition is also similar to the de Almeida-Thouless transition, which occurs in spin glasses with a magnetic field. However, the Gardner transition is more general and does not require an external field.
The Gardner transition has been observed experimentally in granular materials, which are composed of macroscopic grains that interact via frictional contact forces. When these materials are compressed and vibrated, they can exhibit signatures of the Gardner transition, such as a large number of nearby mechanically stable configurations, a broad distribution of contact forces, and a slow relaxation of the stress. The Gardner transition in granular materials may have implications for understanding the rheology and flow of these systems, as well as their response to external stimuli.
The Gardner transition is an intriguing and challenging topic in condensed matter physics, as it reveals the rich and subtle behavior of disordered systems. It also connects different fields of research, such as glass physics, spin glass theory, and granular matter. The Gardner transition may provide new insights into the nature of the glass transition, which is one of the most fundamental and unresolved problems in physics.
