Physical Sciences and Mathematics Commons^™

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the …

Microscopic Theory Of Network Glasses, Randall Hall, Peter Wolynes

Randall W. Hall

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are “strong” while van der Waals liquids without coordination are “fragile.”

The Sign Learning Kink (Silk) Based Quantum Monte Carlo (Qmc), Xiaoyao Ma, Frank Loffler, Randall W. Hall, Karol Kowalski, Mark Jarrell, Juana Moreno

Randall W. Hall