Elasticity and response in nearly isostatic periodic lattices.
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* approximately square root of k' and length l* approximately square root of 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.
Souslov
Anton
A
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Liu
Andrea J
AJ
Lubensky
T C
TC