Spin glasses in finite dimensions

6 problems

• Existence of a de Almeida-Thouless line in three dimensions

  Contested

  In the solvable infinite-range model a spin glass stays glassy in a magnetic field up to a critical line in the field-temperature plane, the de Almeida-Thouless (AT) line. Whether such a line exists in three dimensions is a direct test between the competing theories.

• Fate of the de Almeida-Thouless line as dimension approaches six

  Contested

  Above six dimensions spin-glass theory becomes simple and the field-driven transition certainly exists. One prediction says it disappears exactly as the dimension drops to six; if so, it cannot exist in three dimensions.

• Spin-chirality decoupling in the 3D Heisenberg spin glass

  Contested

  In spin glasses whose atomic magnets can point in any direction, a second quantity, the chirality (the handedness of how neighboring spins twist), can also freeze. The question is whether spins and chiralities freeze at the same temperature or chiralities freeze first.

• Replica symmetry breaking or droplets in the 3D Edwards-Anderson model

  Contested

  Below its freezing temperature, does a three-dimensional spin glass have many distinct frozen states, as in the solvable infinite-range model, or essentially one state and its mirror image? The two pictures predict different responses to small changes in temperature or magnetic field.

• Exact lower critical dimension of the Ising spin glass

  Open

  Below a certain space dimension, magnets with random-sign interactions never freeze into a glass at any nonzero temperature. That dimension lies between two and three, and a conjecture says it is exactly two and a half.

• Mechanism of memory and rejuvenation in aging spin glasses

  Partially resolved

  A spin glass cooled, held at one temperature and then cooled further appears to start aging anew (rejuvenation), yet it recovers its earlier state when reheated (memory). Which microscopic processes produce both effects at once is not settled.