  Recently in paper [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)] the
experimental observation of the Lee-Yang zeros of an Ising-type spin-1/2 bath,
by measuring the coherence of a probe spin, was reported. We generalize this
problem to the case of an arbitrary high-spin bath. Namely, we consider the
evolution of a probe arbitrary spin which interacts with bath composed by N
arbitrary spins. As a result, the connection between the observed values of the
probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is
found. We apply these results to some models, namely, a triangle spin cluster,
the Ising model with a long-range interaction and the 1D Ising model with
nearest-neighbor interaction. Also we propose the implementation of these
models on real physical systems.
