  The $n$-index R\'enyi mutual information and transfer entropy for the
two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the
thermodynamic limit are derived as functions of thermodynamic quantities. By
means of Monte Carlo simulations with the Wolff algorithm, we calculate the
information flows in the Ising model with the Metropolis dynamics and the
Glauber dynamics. We find that, not only the global R\'enyi transfer entropy,
but also the pairwise R\'enyi transfer entropy peaks in the disorder phase.
Therefore, the R\'enyi information flows may be used as better tools than the
Shannon counterparts in the study of phase transitions in complex dynamical
systems.
