  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 two disordered
solid phases that have similar structural features but that 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.
