  We apply realization theory of non-commutative rational multipliers of the
Fock space, or free Hardy space of square--summable power series in several
non-commuting variables to the convex analysis of states on the Cuntz algebra.
We show, in particular, that a large class of Cuntz states which arise as the
`non-commutative Clark measures' of isometric NC rational multipliers are peak
states for Popescu's free disk algebra in the sense of Clou\^atre and Thompson.
