Although discussed since ancient times, the origin of rigidity in
materials remains a disputed topic. How can a material be rigid when
its atoms must be in perpetual motion? The finite temperature
liquid-to-solid transition is discontinuous, owing to the accompanying
breaking of the translational symmetry. The periodicity and anisotropy
of the solid, if any, render the transition sharp but are not
essential. Rigid aperiodic solids range from piles of sand, for which
thermal effects are indeed negligible, to glasses, which are rigid
despite vigorous thermal motion at the microscopic level. The former
are mechanically jammed, while the latter are made by thermally
quenching an equilibrated liquid. The thermal, rheological, and
electronic behaviors of glasses exhibit many universal features. I
will explain how these can be understood quantitatively. The latter
quantitative description excludes jamming as the mechanism of the
structural glass transition and crystal formation alike. In fact,
jammed and finite-temperature aperiodic solids can be thought of
states as two distinct phases on a generalized phase diagram
containing off-equilibrium states.
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