Exact results on spin glass models

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.