Cumulative Geometric Frustration and the Intrinsic Approach in Continuous Systems

Geometric frustration results from an incompatibility between the locally favored arrangement of the constituents in a system and the geometric properties of the space in which it resides. It naturally arises in a variety of fields ranging from macro-molecular assemblies to liquid crystals to spin models, yet in distinct systems geometric frustration may be associated with different phenomena. For example, in liquid crystals frustration may lead to spontaneous size limitation and to a unique ground state whose energy grows super-extensively, while for the Ising antiferromagnet on triangular lattice frustration leads to a highly degenerate ground state of extensive energy.    

In this talk, I will discuss how the intrinsic approach, in which matter is described only through local properties, leads to a general framework in which the geometric compatibility conditions assume a central role. This framework, in particular, allows predicting the super-extensive energy exponent for sufficiently small systems, without the need to explicitly solve the system's ground state. I will discuss the application of the framework to growing elastic bodies, frustrated liquid crystals, and to explain the origin of the distinct behavior in frustrated spin systems.