Andrea Cavagna et al 2003 J. Phys. A: Math. Gen. 36 1175 doi:10.1088/0305-4470/36/5/301
Andrea Cavagna1, Irene Giardina1, Giorgio Parisi1 and Marc Mézard2
Show affiliationsWe revisit two classic Thouless–Anderson–Palmer (TAP) studies of the Sherrington–Kirkpatrick model (Bray A J and Moore M A 1980 J. Phys. C: Solid State Phys. 13 L469; De Dominicis C and Young A P 1983 J. Phys. A: Math. Gen. 16 2063). By using the Becchi–Rouet–Stora–Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed calculation of the TAP complexity is formally identical to the quenched thermodynamic calculation of the free energy at one step level of replica symmetry breaking. The complexity we obtain by means of the BRST symmetry turns out to be considerably smaller than the previous non-symmetric value.
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 5 (7 February 2003)
Received 5 November 2002
Published 22 January 2003
Andrea Cavagna et al 2003 J. Phys. A: Math. Gen. 36 1175
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