Condensed Matter Theory

Abstract:

Many classical, geometrically frustrated antiferromagnets have macroscopically degenerate ground states. In a class of three-dimensional systems, the set of degenerate ground states has power-law correlations and is an example of a Coulomb phase. We investigate Neel ordering from such a Coulomb phase, induced by weak additional interactions that lift the degeneracy. We show that the critical point belongs to a universality class that is different from the one for the equivalent transition out of the paramagnetic phase, and that it is characterised by effective long-range interactions; alternatively, ordering may be discontinuous. We suggest that a transition of this type may be realised by applying uniaxial stress to a pyrochlore antiferromagnet.

Abstract:

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.