Let OK be a complete discrete valuation ring of mixed
characteristic with perfect residue field, endowed with its canonical
log-structure. We prove that log p-divisible groups over OK
correspond to Dieudonn\'e crystals on the absolute log-prismatic site of
OK endowed with the Kummer log-flat topology. The proof uses
log-descent to reduce the problem to the classical prismatic correspondence,
recently established by Ansch\"utz-Le Bras.Comment: 19 page