Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 68-75 |
| Number of pages | 8 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 306 |
| DOIs | |
| Publication status | Published - 2002 Apr 1 |
| Externally published | Yes |
| Event | 21th IUPAP Conference on Invited Papares (STATPHYS 21) - Cancun, Mexico Duration: 2001 Jul 15 → 2001 Jul 21 |
Keywords
- Gauge theory
- Ising model
- Random-phase XY model
- Spin glass
- Spin wave theory
- Villain model
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics
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Nishimori, H. (2002). Exact results on spin glass models. Physica A: Statistical Mechanics and its Applications, 306, 68-75. https://doi.org/10.1016/S0378-4371(02)00486-7