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Importance of the 'Higgs' Amplitude Mode in Understanding the "Ideal Glass Transition" and the Kauzmann Entropy Paradox at the Four-Dimensional Crystal/Glass Quantum Critical Point
Caroline S. Gorham, David E. Laughlin
In this article, a theoretical description of the "ideal glass transition" is approached upon the adoption of a quaternion orientational order parameter. Unlike first-order phase t…
On the Formation of Solid States Beyond Perfect Crystals: Quasicrystals, Geometrically-Frustrated Crystals and Glasses
Caroline S. Gorham, David E. Laughlin
There are three kinds of solid states of matter that can exist in physical space: quasicrystalline (quasiperiodic), crystalline (periodic) and amorphous (aperiodic). Herein, we con…
Solidification of Icosahedral Quasicrystals: Viewpoint Based on a Quaternion Orientational Order Parameter and the Formation of the E8 Lattice
Caroline S. Gorham, David E. Laughlin
In this article, the solidification phase transition between isotropic liquids and icosahedral quasicrystalline structures is classified by the application of a quaternion orientat…
Quantized Hall Effect Phenomena and Topological-Order in 4D Josephson Junction Arrays in the Vicinity of a Quantum Phase Transition
Caroline S. Gorham, David E. Laughlin
Recently, generalizations of quantum Hall effects (QHE) have been made from 2D to 4D and 8D by considering their mathematical frameworks within complex (C), quaternion (H) and octo…