Our work on curved space and frustration with Gilles Tarjus at the Université Pierre et Marie Curie in Paris is
going to appear published in Physical Review Letters, 118, 215501.
In it, we provide a test of one of the competing theories for the origins of the glass transition: this is geometric frustration, i.e. the idea that the slowing down observed in glass forming liquids goes hand in hand with the formation of particular non-cristalline geometric motifs, that increase in size as the liquids are cooled.
We test this on the most favourable ground for the theory, which is a curved manifold. We do this for the first time in three dimensions, observing the structural evolution of a glass former on the surface of a sphere embedded in four dimensions (This is a funny space to work in. A beautiful way to visualise such a hypersurface is to use the so-called two-ball construction, see image above, which nicely matches with the vision of the universe that Dante and his teacher Brunetto Latini had).
What we find is that geometrical motifs become gradually unfrustrated as the curvature increases (which is compatible with the basic assumptions of geometric frustration) and ordered phases (with some tricky defects, that we discuss in the Supplemental Material) spontaneously form for low enough temperatures. However, the size of the domains in such motifs is tightly coupled with the slowing down only for very strong curvatures, making geometric frustration just one of the mechanisms that eventually play a role in realistic glass-forming fluids (that exist in our ordinary Euclidean space).