Exact results on spin glass models
arXiv:cond-mat/0201056 · doi:10.1016/S0378-4371(02)00486-7
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.
9 pages, Proceedings of STATPHYS21, to be published in Physica A
Cited by in corpus (4)
- Magnetic and glassy transitions in the square-lattice XY model with random phase shifts
- Continuous symmetry breaking along the Nishimori line
- Error threshold in optimal coding, numerical criteria and classes of universalities for complexity
- Quasi-long-range order in the 2D XY model with random phase shifts