Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin glasses in finite dimensions, such as the exact energy, correlation identities and a functional relation between the distribution functions of ferromagnetic and spin glass order parameters. This last relation is useful to prove that the phase space is not complex on a line in the phase diagram. The spin wave theory neglecting periodicity is shown to give exact results for the Villain model on a line in the phase diagram. Implications of this fact on the renormalization-group results for the random-phase XY/Villain model in two dimensions are discussed.
|ジャーナル||Physica A: Statistical Mechanics and its Applications|
|出版物ステータス||Published - 2002 4 1|
|イベント||21th IUPAP Conference on Invited Papares (STATPHYS 21) - Cancun, Mexico|
継続期間: 2001 7 15 → 2001 7 21
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics