  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. \end{abstract}
