  In 1979, G. Parisi predicted a variational formula for the thermodynamic
limit of the free energy in the Sherrington-Kirkpatrick model and described the
role played by its minimizer. This formula was verified in the seminal work of
Talagrand and later generalized to the mixed p-spin models by Panchenko. In
this paper, we prove that the minimizer in Parisi's formula is unique at any
temperature and external field by establishing the strict convexity of the
Parisi functional.
