Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model
Disordered Systems and Neural Networks
2008-09-16 v1 Statistical Mechanics
Abstract
We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field.
Keywords
Cite
@article{arxiv.0711.3384,
title = {Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model},
author = {V Janis and A. Klic and M. Ringel},
journal= {arXiv preprint arXiv:0711.3384},
year = {2008}
}
Comments
15 pages, 4 EPS figures