Spin-glass transition in a magnetic field

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 TJH) 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 nonequilibrium 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 occurs only at T=0. The effect of magnetic fields on the zero-temperature transition is briefly discussed. Experimentally, spin- glass behaviour does seem to occur in the presence of magnetic fields below a critical temperature T_C(H). Possible interpretations of the experimental results are summarized.