Double criticality of the Sherrington-Kirkpatrick model at T=0.
Numerical results up to the 42nd order of replica-symmetry breaking (RSB) are used to predict the singular structure of the Sherrington-Kirkpatrick spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and a=infinity are shown to be two critical points for infinity-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are obtained with unprecedented accuracy.
Oppermann
R
R
Institut für Theoretische Physik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany.
Schmidt
M J
MJ
Sherrington
D
D