  In this note we study the deformation theory of periodic (logarithmic)
Higgs-de Rham flows. Under suitable numerical assumptions, this is equivalent
to the deformation theory of torsion (logarithmic) Fontaine-Faltings modules.
As an application, we formulate an \emph{ordinarity} condition, which provides
a sufficient condition for a $p^n$-torsion crystalline representation to deform
to a $p^{n+1}$-torsion crystalline representation.
