V Janiš et al 2008 J. Phys. A: Math. Theor. 41 324004 doi:10.1088/1751-8113/41/32/324004
V Janiš, A Klíč and M Ringel
Show affiliationsWe 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.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 32 (15 August 2008)
Received 20 November 2007, in final form 14 January 2008
Published 30 July 2008
V Janiš et al 2008 J. Phys. A: Math. Theor. 41 324004
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