Abstract
The square lattice with nearest neighbor central-force springs is isostatic and does not support shear. Using the coherent potential approximation (CPA), we study how the random addition, with probability (), of next-nearest-neighbor (NNN) springs restores rigidity and affects phonon structure. The CPA effective NNN spring constant , equivalent to the complex shear modulus , obeys the scaling relation, , at small , where and , implying nonaffine elastic response at small and the breakdown of plane-wave states beyond the Ioffe-Regel limit at . We identify a divergent length , and we relate these results to jamming.
- Received 14 September 2009
DOI:https://doi.org/10.1103/PhysRevLett.104.085504
©2010 American Physical Society