A New Perspective on the Kauzmann Entropy Paradox: A Crystal/Glass Critical Point in Four- and Three-Dimensions

In this article, a new perspective on the Kauzmann point is presented. 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 model solidifying liquids by using a quaternion orientational order parameter and find that the Kauzmann point is a critical point that exists to separate crystalline and non-crystalline solid states. We identify the Kauzmann point as a first-order critical point, and suggest that it belongs to quaternion ordered systems that exist in four- or three-dimensions. This “Kauzmann critical point” can be considered to be a higher-dimensional analogue to the superfluid-to-Mott insulator quantum phase transition that occurs in two- and one-dimensional complex ordered systems. Such 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 critical point is a consequence of the discrete change of the topology of the ground state manifold of the quaternion order parameter field that applies to crystalline and non-crystalline solids.