  We calculate the joint min--max distribution and the Edwards-Anderson's order
parameter for the circular model of $1 / f$-noise. Both quantities, as well as
generalisations, are obtained exactly by combining the freezing-duality
conjecture and Jack-polynomial techniques. Numerical checks come with
significantly improved control of finite-size effects in the glassy phase, and
the results convincingly validate the freezing-duality conjecture. Application
to diffusive dynamics is discussed. We also provide a formula for the
pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for
minimum/maximum which applies to any logarithmic random energy model.
