Abstract
Abstract Studies of the spin-glass phase transition in the presence of magnetic fields are reviewed. Most of the theoretical results on the existence of such a transition and its properties are derived from the mean-field theory of spin glasses, which describes infinite-range systems. In this limit, there exists a line T c(H) which separates the region (T > T c(H)) of a unique equilibrium paramagnetic state and the region (T > T c(H)) where ergodicity is broken and the system is frozen in one of many equilibrium spin-glass states. The singularities in both equilibrium and non-equilibrium quantities at the finite-field transition are described. In vector spin glasses this transition is associated with the freezing of transverse degrees of freedom. However, weak random anisotropy may induce a cross-over to Ising behaviour if it is sufficiently strong compared to the magnetic field. In two-dimensional systems with short-range forces, and perhaps in three-dimensional systems as well, the spin-glass transition...
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