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