  The earlier times of evolution of a magnetic system contain more information
than we can imagine. Capturing correlation matrices G of different time
evolutions of a simple testbed spin system, as the Ising model, we analyzed the
density of eigenvalues of G^{T}G for different temperatures. We observe a
transition of the shape of the distribution that presents a gap of eigenvalues
from critical temperature with a continuous migration to the Marchenko-Pastur
law for the paramagnetic phase. We consider the analysis a promising method to
be applied in other spin systems to characterize phase transitions. Our
approach is different from alternatives in the literature since it uses the
magnetization matrix and not the spatial matrix of spins.
