Frustration(s) and the ice rule: From natural materials to the deliberate design of exotic behaviors

Abstract

The ice rule has a long, interesting history, one that proved most influential to thermodynamics, physical chemistry, statistical mechanics, magnetism, material science, and soft matter. First introduced to solve the mystery of the residual entropy in water ice, it has motivated an entire set of exactly solvable problems in statistical mechanics and applied mathematics. It was then recognized in exotic magnets at low temperature, and designed in new artificial frustrated systems, both magnetic and colloidal. As new classes of artificial ice rule materials are being presented, dedicated geometries are proposed to generate new, exotic collective behaviors, often not found in natural systems. There, a deeper understanding of the origin of the ice rule from different forms of frustration can be exploited for design of unusual phases.