Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model
Alessia Annibale, Andrea Cavagna, Irene Giardina, Giorgio Parisi
TL;DR
This paper uses BRST supersymmetry to compute the quenched complexity of TAP states in the SK model, linking it to the Legendre transform of the static free energy at the largest RSB point.
Contribution
It demonstrates that the BRST complexity equals the Legendre transform of the free energy, providing a novel analytical connection in spin glass theory.
Findings
BRST complexity matches the Legendre transform of the free energy.
Established a link between quenched complexity and static free energy.
Provided a new analytical method for studying TAP states in the SK model.
Abstract
By using the BRST supersymmetry we compute the quenched complexity of the TAP states in the SK model. We prove that the BRST complexity is equal to the Legendre transform of the static free energy with respect to the largest replica symmetry breaking point of its overlap matrix.
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