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The high-temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even in this limit. Here, we demonstrate that the spin noise power spectrum of these fluctuations can undergo discontinuous changes as a function of an external magnetic field. As a simple illustration, we consider a model of Ising-like long-range spin-spin interactions with a transverse magnetic field as a control parameter. This system undergoes a phase transition associated with disappearance of the noise power peak responsible for the most detrimental decoherence effect of the interactions.
Gorshkov et al. (Fri,) studied this question.