Geometrical frustration (nonfiction)

Geometrical frustration of an icosahedron.

In condensed matter physics, the term geometrical frustration (or simply frustration) refers to a phenomenon, where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces (each one favoring rather simple, but different structures) lead to quite complex structures.

As a consequence of the frustration in the geometry or in the forces, a plenitude of distinct ground states may result at zero temperature, and usual thermal ordering may be suppressed at higher temperatures.

Much studied examples are amorphous materials, glasses, or dilute magnets.

The term frustration, in the context of magnetic systems, has been introduced by Gerard Toulouse (1977).

Frustrated magnetic systems had been studied earlier, including G. H. Wannier's study of the Ising model on a triangular lattice with nearest-neighbor spins coupled antiferromagnetically (published 1950).

In the News

Nest of empty Klein bottles after an Extract of Radium lucubration.
David Hedison at risk of geometrical frustration.
Wax seal on feeding tube enables Gnotilus to secrete geometry solvent directly into ENIAC.