[source] Geometrically frustrated systems cannot satisfy all local constraints, and thus, they remain disordered down to zero temperature, with a highly degenerate ground state. If entropy of fluctuations about each ground-state configuration slightly varies, then the configuration with the highest entropy will be thermodynamically selected in an order by disorder effect.

When the packing density of a buckled colloidal monolayer approaches close packing, the free-volume-dominated free energy of the system causes neighboring spheres to prefer touching opposite walls, giving rise to effective antiferromagnetic interactions.

This system exhibits the same ground state degeneracy as the Ising antiferromagnet on a deformable triangular lattice, which is given by straight stripes or any set of zigzagging stripes configurations of alternating up and down spheres.

We study ordering in buckled monolayers when the density is somewhat smaller than close packing. To this end we developed a real-space expansion method to compute the entropy originating from the collective fluctuation of different subsets of mobile particles. By modelling the colloidal particles as hard or soft spheres with different inter-particle potentials, we discovered that including attraction reverses the effect of fluctuations on the ground state selection mechanism, in a manner that is linked to local packing considerations. This supports the geometric origin of entropy in jammed sphere packings and provides a tool for designing self-assembled colloidal structures.

Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice

Y. Shokef, A. Souslov, and T.C. Lubensky**Proceedings of the National Academy of Sciences of the USA** 108, 11804 (2011)

Attraction controls the inversion of order by disorder in buckled colloidal monolayers

F. Leoni and Y. Shokef**Physical Review Letters** 118, 218002 (2017)