Charbonneau, P; Kurchan, J; Parisi, G; Urbani, P; Zamponi, F, *Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution*,
Journal of Statistical Mechanics: Theory and Experiment, vol. 2014 no. 10
(October, 2014),
pp. P10009-P10009 [2549], [doi] .
**Abstract:**

*We derive the general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus showing that the analogy between spin glass models and structural glasses conjectured by Kirkpatrick, Thirumalai, and Wolynes is indeed realized in a strong sense in the mean field limit. We also suggest how the computation could be generalized in an approximate way to finite dimensional hard spheres. We present preliminary results obtained from the solution of these equations. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly the critical exponents associated to scaling around the jamming transition, which are missed by the 1RSB solution.*