Stress distribution and the fragility of supercooled melts

We formulate a minimal ansatz for local stress distribution in a solid that includes the possibility of strongly anharmonic short-length motions. We discover a broken-symmetry metastable phase that exhibits an aperiodic, frozen-in stress distribution. This aperiodic metastable phase is characterized by many distinct, nearly degenerate configurations. The activated transitions between the configurations are mapped onto the dynamics of a long-range classical Heisenberg model with 6-component spins and anisotropic couplings. We argue the metastable phase corresponds to a deeply supercooled nonpolymeric, nonmetallic liquid and further establish an order parameter for the glass-to-crystal transition. The spin model itself exhibits a continuous range of behaviors between two limits corresponding to frozen-in shear and uniform compression/dilation, respectively. The two regimes are separated by a continuous transition controlled by the anisotropy in the spin-spin interaction, which is directly related to the Poisson ratio sigma of the material. The latter ratio and the ultraviolet cutoff of the theory determine the liquid configurational entropy. Our results suggest that liquid's fragility depends on the Poisson ratio in a nonmonotonic way. The present ansatz provides a microscopic framework for computing the configurational entropy and relaxational spectrum of specific substances.