Hierarchical structure of the energy landscape in the Voronoi model of dense tissue

The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature, the model exhibits a disordered solid structure with no evidence of a rigidity transition. Here, we investigate the properties of the energy landscape in this limit. We find that the structure of the energy landscape changes as a function of the preferred shape parameter of the cells p(0). We find two disordered solid phases that have similar structural features but differ in the ultrametricity of their energy landscapes; the crossover between these two states shares phenomenological properties with a Gardner transition. We further highlight how the metric used to calculate distances between configurations influences the ability to detect hierarchical arrangements of basins in the energy landscape.