Fig. 3: Spatial correlations of the topological defects.
a–c Pair correlation functions for + + , − − , and + − defect pairs at different values of ω, in which the frequency labels are given on the right-hand side of panel (a). Curves for ω > 0.259 are shifted downward by multiple factors of 0.25 for visibility. The straight dashed line in panels (a) and (b) is a power-law with exponent df − d = − 5/3, which gives for d = 3 a fractal dimension of df = 4/3. The vertical dotted line shows the correlation hole, which is located at \(r\approx \sqrt{2}/2\). d The ω-dependence of the height of the main peak in gαβ(r; ω). e Inverse of the position of the level-off ξ in g++(r; ω) as a function of frequency. The data at low frequency display the expected linear behavior (dashed line) with a slope given by the average velocity-of-sound that can be calculated directly from the elastic moduli (Supplementary Table 1).
