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arXiv · 0803.3918

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

Reinhold Oppermann·Manuel J. Schmidt
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Abstract

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.

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Reinhold Oppermann, Manuel J. Schmidt. 2008-04-29. Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model. https://doi.org/10.1103/physreve.78.061124

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