Equilibrium behavior of the spin-glass ordered phase

A phenomenological theory of the ordered phase of short-range Ising spin glasses is developed in terms of droplet excitations and presented in detail. These excitations have free energies with a broad distribution whose characteristic magnitude grows with length scale L as $L^{\theta }$. A small fraction of droplets of all scales are thermally active; these dominate much of the physics. The mean-square correlation functions are found to decay with distance as 1/$r^{\theta }$ for all T<$T_c$ and the autocorrelations decay logarithmically with time because of large activation barriers for creation and annihilation of the droplet excitations. A renormalization procedure is sketched in order to define excitations at positive temperature. It is found that the long-distance equilibrium correlation functions are extremely sensitive to small temperature changes, yielding breakdown of certain relations between fluctuations and thermodynamic derivatives. The behavior near to the critical temperature is discussed and some of the ideas are extended to systems with power-law interactions and to spin glasses with X-Y or Heisenberg symmetry. The inequality θ≤(d-1)/2 is also derived.