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Rigidity transition in amorphous media
Contrarily to cristalline solids, amorphous media (glasses, emulsions,
granular media, suspensions, foam, etc) do not present any long range translational order. However, they can resist shear and therefore behave mechanically as solid materials. To make them flow as a liquid, one has, depending on the material, to increase temperature, to decrease the volume fraction or to submit it to a large enough shear stress. Is this transition between solid-like and liquid-like behaviours, called the rigidity transition, a true phase transition ? Does it present the characteristics of critical phenomena (divergent correlation time and length, dynamic dominated by fluctuations, critical exponent) ? After a short introduction on ordinary liquids and cristalline solids, I will
review the characteristics of the three transitions that appear in the literature devoted to these questions : the glass transition, controlled by entropy, the elasto-plastic depinning transition, controlled by enthalpy, and the jamming transition, controlled by geometry. I will exhibit different links between these transitions, that may shed some light on
their nature and their properties.