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A New Perspective on the Kauzmann Entropy Paradox: A Four-Dimensional Crystal/Glass Quantum Critical Point
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1  Carnegie Mellon University


In this article, a new perspective on the Kauzmann point is presented. We model the solidifying liquid by a quaternion orientational order parameter and find that the Kauzmann point is analogous to a quantum critical point. The “ideal glass transition" that occurs at the Kauzmann temperature is the point at which the configurational entropy of an undercooled metastable liquid equals that of its crystalline counterpart. We identify this point as a first order quantum critical point. We suggest that this quantum critical point belongs to quaternion ordered systems that exist in four- and three-dimensions. This “Kauzmann quantum critical point” can be considered to be a higher-dimensional analogue to the superfluid-to-Mott insulator quantum phase transition which occurs in two- and one-dimensional complex ordered systems. Such quantum critical points are driven by tuning a non-thermal frustration parameter, and result due to characteristic softening of a ‘Higgs’ type mode that corresponds to amplitude fluctuations of the order parameter. The first-order nature of the finite temperature Kauzmann quantum critical point is seen as a consequence of the discrete change of the topology of the ground state manifold that applies to crystalline and non-crystalline solid states.

Keywords: Kauzmann entropy paradox; topological order; Higg's amplitude mode; solidification; quaternion order parameter