Geometrical Frustration, Spin Ice and Negative Thermal Expansion - The Physics of Underconstraint

The idea that some systems could have a thermodynamically-large number of accessible ground states was presaged in the work of Pauling on ice. With the advent of spin glasses, the methodology for describing ground states changed dramatically, and in particular it was realized that the observed slow dynamics were due to relaxation among a large number of nearly degenerate ground states. Now the accepted wisdom is that both "frustration", as well as structural disorder, is responsible for spin glass behavior. However, well before spin-glasses were identified as a distinct class of systems, it had been appreciated that even for structurally-periodic systems, bond frustration could lead to a thermodynamically-large number of states. There is now a well-defined class of magnets which display effects of macroscopic ground state degeneracy. This class of geometrically frustrated magnets presents some new paradigms with which to view condensed matter systems - marginal underconstraint and downward shift of spectral weight. We discuss possible realizations of these phenomena in both spin ice and also outside the context of local-moment magnetism.