Geometric Frustration and the Intrinsic Approach in Soft Condensed Matter

Geometric frustration arises whenever the constituents of a physical assembly are endowed with two or more mutually contradicting tendencies. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large morphological variations and exotic response properties. These unique characteristics can be shown to be a direct outcome of the geometric frustration. However, not all frustrated systems are alike. Some frustrated systems, such as the Ising anti-ferromagnet on a triangular lattice do not exhibit any of the above characteristics. We refer to such frustration as non-cumulative.

 In this talk I will discuss how the intrinsic approach, in which matter is described only though local properties, allows to distinguish between cumulative and non-cumulative frustration, and predicts the super-extensive energy exponent for sufficiently small systems. I will present how the intrinsic approach finds application in the elasticity of growing bodies, in the theory of frustrated liquid crystals and in the formation of twisted molecular crystals. I will conclude by presenting a variant of the XY- model that exhibits cumulative geometric frustration.