  As a universal quantum character of quantum correlation, the freezing
phenomenon is researched by geometry and quantum discord methods, respectively.
In this paper, the properties of R`enyi discord is studied for two independent
Dimer System coupled to two correlated Fermi-spin environments under the
non-Markovian condition. We further demonstrate that the freezing behaviors
still exist for R`enyi discord and study the effects of different parameters on
this behaviors.
