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

TL;DR

This paper explores the energy landscape of the Voronoi model for dense tissues, revealing two disordered solid phases with different ultrametricity and a transition akin to the Gardner transition, influenced by the choice of metric.

Contribution

It uncovers the hierarchical structure of the energy landscape in the Voronoi model and identifies a Gardner-like transition between two disordered solid phases.

Findings

Identified two disordered solid phases with different ultrametricity

Discovered a crossover sharing properties with the Gardner transition

Showed the influence of metric choice on detecting hierarchical basins

Abstract

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.