Dipole-induced transition in 3 dimensions.

The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important "topological" transitions are restricted to 2-dimensions. Here, we present a genuine dipole-induced transition in the 3-dimensional response of (athermal) amorphous solids to applied strain. Similarly to the existence of a hexatic phase between normal solid and fluid, we identify an intermediate phase between a phase of normal elastic response at high pressure, and fluid matter at zero pressure. The mechanical response in the intermediate phase is accompanied by plasticity that is generically associated with "nonaffine" quadrupolar events seen in the resulting displacement field. Gradients of the quadrupolar fields act as dipole charges that screen elasticity, breaking both translational and chiral symmetries. We highlight angular correlations that exhibit diverging correlation lengths at this transition and determine the critical scaling exponents.