Magnetic-field symmetry breaking in spin glasses*

Time-reversal symmetry is spontaneously broken in spin glasses below their glass temperature. Under such conditions, the standard assumption about the equivalence of the most standard protocols (i.e. no big difference between switching the field on or off, as it is sometimes said) is not really justified. In fact, we show here that the spin-glass coherence  length behaves differently in the zero-field-cooled (ZFC, magnetic field is turned on) and thermoremanent-magnetization (TRM, magnetic field is turned off) protocols. This conclusion is reached through experiments, carried out on two CuMn single-crystal samples, and through massive simulations on the Janus~II dedicated supercomputer. In agreement with the predictions of a simple dynamical model that assumes that the ultrametric tree of states survives the switching-on of the magnetic field, we conclude that (all parameters being kept equal) the spin-glass coherence length is larger in the ZFC protocol. This has implications for the extended principle of superposition, which, while holding at H = 0, breaks down for finite magnetic fields. Preliminary simulation results support this observation.