# Liu-Nagel phase diagrams in infinite dimension

## TL;DR

This paper investigates the phase behavior of harmonic soft spheres in infinite dimensions, revealing how perturbations like shear and compression induce Gardner transitions, leading to marginally stable amorphous solids.

## Contribution

It demonstrates that perturbations such as shear and compression induce Gardner transitions in harmonic soft spheres, extending understanding of glass stability and marginality in infinite dimensions.

## Key findings

- Gardner transition occurs under cooling, compression, and shear.
- Reduced glass stability favors Gardner transition.
- Strong or weak perturbations can induce Gardner transition.

## Abstract

We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous solid as found for Hard Spheres systems. A general outcome of our results is that a reduced stability of the glass favors the appearance of the Gardner transition. Therefore using strong perturbations, e.g. shear and compression, on standard glasses or using weak perturbations on weakly stable glasses, e.g. the ones prepared close to the jamming point, are the generic ways to induce a Gardner transition. The formalism that we discuss allows to study general perturbations, including strain deformations that are important to study soft glassy rheology at the mean field level.