Renormalization of elastic quadrupoles in amorphous solids
arXiv:1912.05970 · doi:10.1103/PhysRevE.101.043002
Abstract
Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the model problem of an elastic continuum with quadrupolar defects, at finite temperature. This problem is posed and the collective behavior of the defects is analytically investigated. Using both renormalization group and field-theoretic techniques, it is found that the model has a yielding/melting transition of spinodal type.
arXiv comment10 pages + 7 pages SI; v2: Appendix added with derivation of effective Hamiltonian, expanded discussion of RG flow, field theory generalized. v3: expanded discussion, table of symbols added
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