Geometric Frustration and the Intrinsic Approach in Soft Condensed Matter
Deducing the emergent behavior of a material from the properties of its molecular or atomic constituents is one of the greatest challenges of condensed matter theory. Considering many-body systems with highly cooperative ground states renders this task even more challenging. Geometrically frustrated assemblies are comprised of ill-fitting constituents that are associated with two or more tendencies that cannot be simultaneously reconciled, and thus lack a stress free rest state. The ground state of frustrated assemblies is highly cooperative, leading them to exhibit super-extensive energy growth, filamentation, size limitation and exotic response properties. Such systems arise in naturally occurring structures in biology and organic chemistry as well as in manmade synthetic materials.
In this talk I will discuss how the intrinsic approach, in which matter is described only through local properties available to an observer within the material, overcomes the lack of a stress free rest state for frustrated assemblies and leads to a general framework. This framework in particular allows predicting the super-extensive energy exponent for sufficiently small systems. I will discuss its application to several specific systems exhibiting geometric frustration: growing elastic bodies, frustrated liquid crystals and twisted molecular crystals.