Orientational fluctuations of amorphous nematogenic solids

Amorphous nematogenic solids (ANS) are media comprising rod-like nematogens that have been randomly linked to form elastically deformable macroscopic networks. ~Classes of ANS include chemical nematogen gels (i.e., networks of small molecules) and liquid crystalline elastomers (built from crosslinked nematogen-containing macromolecules), as well as biophysical networks such as those composed of actin filaments. ~We use a method inspired by the cavity approach to construct a replica free energy for these random systems, and investigate the correlations of the thermal fluctuations of the orientational alignment of the nematogens at spatially separated points. ~We identify two qualitatively distinct regimes: (a) a weakly localized regime, in which the correlations decay exponentially with separation; and (b) a strongly localized regime, characterized by correlations that also decay but oscillate as they do.