The Gardner Glass

The application of the replica method to the analysis of mean-field models of packings of particles has allowed the construction of a theory of amorphous solids in infinite dimensions. In particular, the theory predicts that glassy states can undergo a replica symmetry breaking transition at low temperature. This RSB transition within a glass state is called Gardner transition in analogy with the RSB transition of the ideal glass state in a certain class of mean-field spin glass models and, after the solution of structural glass models in infinite dimensions, it has emerged as a crucial scenario for understanding the low temperature properties of amorphous solids. The chapter focus on recent theoretical and numerical results on this topic. In the first part, Pierfrancesco Urbani outlines the ideas that lead to the mean-field theory of the Gardner transition for infinite-dimensional amorphous solids, and the consequent main achievements obtained within such a theory. In the second part, Yuliang Jin and Hajime Yoshino overview methods and results of the numerical investigations of the nature of the Gardner phase in finite-dimensional packings, and discuss evidences of the validity of some mean-field predictions beyond the infinite-dimensional limit.