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A scaling theory of replica symmetry breaking (RSB) in the SK-model ispresented in the framework of critical phenomena for the scaling regime ofsmall inverse RSB-orders, small temperatures, small magnetic fields, and nearopposite pseudo-dynamic limits. We employ the pseudo-dynamical picture (PRL98,127201 (2007)) with two critical points, where separated temperature- andmagnetic field-scaling is obtained. An unconventional scaling hypothesis forthe free energy is given, modeling this separated scaling in accordance withdetailed numerical self-consistent solutions for up to 200 orders of RSB. Adivergent correlation-length describes the RSB-criticality as a long-rangecorrelation effect occurring on the pseudo-lattice of RSB-orders.Rational-valued exponents are concluded with high precision from high-order RSBscaling and by using a new fixed point extrapolation method. Power laws,scaling relations, and scaling functions are analyzed.

physical review. e, statistical, nonlinear and soft matter physics

Universality class of replica symmetry breaking, scaling behavior, and  the low-temperature fixed-point order function of the Sherrington-Kirkpatrick  model