Shear rigidity percolation in 2D solid-liquid composites

Shear rigidity percolation is studied on a simple square lattice where a fraction p of the area is filled by an elastic solid, and the rest by liquid. The presence of the liquid is shown to yield a new shear critical exponent τ at the percolation threshold. Through finite-size scaling calculations the value of τ is found to be 1.2±0.1, while similar calculations on solid-vacuum composites yield the 2D elastic critical exponent T=3.4±0.2, in excellent agreement with prior results. The underlying physics of the solid-liquid rigidity percolation is discussed.