PhD defence: Criticality of absorbing phase transitions with long-range interactions in soft matter - Tristan Jocteur (PSM, LIPhy)

The yielding of amorphous materials under applied shear stress and the loss of reversibility in the flow of cyclically sheared suspensions are two soft matter phenomena that, at first glance, appear unrelated. However, when considered as absorbing phase transitions, they reveal strong similarities. Both involve long-range mediated interactions—arising from the material's elasticity in the first case, and from the fluid's viscosity in the second—leading to shared unusual behaviors. The aim of this thesis is therefore to understand the role of these interactions in shaping the specific nature of these two transitions.

To this end, we propose a numerical study of these phenomena using minimal models, in order to determine how the critical behavior evolves as the interaction range is varied. In both cases, this study reveals an increase in the convexity of the transition, a suppression of the divergence of critical fluctuations, and a loss of compactness in the associated avalanches as the interaction range increases. These critical landscapes are then compared to two distinct theoretical frameworks, allowing us to isolate two modes for the propagation of activity in these phenomena: one based on locally induced transport, and another based on non-locally induced diffusion—the latter dominating the behavior of both systems in the infinite-range limit.