Characterizing universal intrinsic mesoscale heterogeneity in the structure and fluctuation correlations of equilibrium amorphous solids

The amorphous solid state (formed, e.g., through the sufficient random crosslinking of macromolecules) is an intrinsically heterogeneous state of matter. It is, therefore, appropriately characterized via various statistical distributions. These distributions are encoded in the order parameter for the amorphous solid state and its fluctuations. For example, it has long been known that the order parameter itself encodes both the fraction of localized particles and the distribution of equilibrium localization lengths [1], and that its fluctuations encode aspects of elastic heterogeneity [2]. Both cases have been addressed using a replica Landau-Wilson description of amorphous solidification [3] and, in the latter case, the Goldstone branch of low-energy fluctuations dictated by the pattern of spontaneous symmetry breaking [2]. We extend this Landau-Wilson-Goldstone approach to obtain a universal statistical characterization of the intrinsic mesoscale structure and fluctuations in the amorphous solid state. This characterization takes the form of a joint distribution governing the statistics of the localization lengths of pairs of particles at fixed mean spatial separation, together with the correlation characteristics of their equilibrium fluctuations. We focus attention on longer-scale particle separations, where the effects of the Goldstone fluctuations are expected to dominate.

[1] H. Castillo, P. M. Goldbart and A. Zippelius, Europhys. Lett. 28, 519-524 (1994).

[2] X. Mao, P.M. Goldbart, X. Xing and A. Zippelius, Europhys. Lett. 80, 26004 (2007).

[3] W. Peng, H.E. Castillo, P.M. Goldbart and A. Zippelius, Phys. Rev. B 57, 839 (1998).