Geometric frustration in soft matter systems
by Pietro Tierno,
This course will review recent advances in the field of geometric frustration, when competing interactions cannot be simultaneously satisfied due to an underlying lattice geometry.
The course will be divided in two parts. The first part will start with a general introductory lecture on the subject, discussing different theoretical models and archetypal examples, as the Ih phase of water ice and its connection with the third law of thermodynamics. Then we will describe the spin ice system, a magnetic analogue of water ice Ih. We will also review geometric frustration in other condensed matter systems, including ferroelectrics, vortices in high Tc superconductors, and magnetic skyrmions, among others. Further we will introduce the artificial spin ice (ASI) system, a convenient method to directly image geometric frustration at the single spin level.
The second part will be centered on the emergence of geometric frustration in soft matter systems. We will then divide this part in two sections: geometric frustration arising from self-assembly, i.e. when the packing or local interactions compete with the global ordering of the system; and that arising from confinements. These two sections are aimed at providing a general overview of geometric frustration effects observed in disparate soft matter systems, including liquid crystals on spherical confinement, compressed elastic sheets, bundles of active filaments and confined microgel particles. The last part will deal with the colloidal ice system, that recently emerged as a powerful tool to engineer and control frustrated states, topological defects and dynamics in artificially designed lattices.