Abstract
Thermally excited circular dislocation loops in a three-dimensional elastic solid renormalize the shear modulus \ensuremath{\mu} to zero at a temperature of the same order of magnitude as the melting temperature of most solids. The vanishing is a universal power law as a function of reduced temperature t: \ensuremath{\mu}\ensuremath{\sim}${\mathit{t}}^{\ensuremath{\gamma}}$,\ensuremath{\gamma}\ensuremath{\sim}0.5. In contrast to dislocation-mediated melting in two dimensions, this is achieved without a sudden proliferation of unbound dislocation loops. It should be possible to experimentally test this behavior with superheated solids.
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