Elasticity and Response in Nearly Isostatic Periodic Lattices

Details Elasticity and Response in Nearly Isostatic Periodic Lattices Elasticity and Response in Nearly Isostatic Periodic Lattices

2009-06-15

arxiv.org/abs/0906.2750v2

Phys. Rev. Lett. 103, 205503 (2009)

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 5 figures, revised text as published in PRL

Scientific paper

10.1103/PhysRevLett.103.205503

The square and kagome lattices with nearest neighbor springs of spring constant $k$ are isostatic with a number of zero-frequency modes that scale with their perimeter. We analytically study the approach to this isostatic limit as the spring constant $k'$ for next-nearest-neighbor bonds vanishes. We identify a characteristic frequency $\omega^* \sim \sqrt{k'}$ and length $l^* \sim \sqrt{k/k'}$ for both lattices. The shear modulus $C_{44}= k'$ of the square lattice vanishes with $k'$, but that for the kagome lattice does not.

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