Fluctuations of the 2-spin SSK model with magnetic field
Benjamin Landon, Philippe Sosoe
TL;DR
This paper investigates the fluctuation behaviors of free energy and overlaps in the quadratic spherical SK model under various magnetic field strengths, confirming several theoretical predictions.
Contribution
It provides a detailed analysis of fluctuation regimes in the spherical SK model with magnetic field, extending previous theoretical predictions.
Findings
Different fluctuation behaviors depending on magnetic field size
Confirmation of Fyodorov-Le Doussal predictions
Alignment with recent work by Baik, Collins-Wildman, Le Doussal, and Wu
Abstract
We analyze the fluctuations of the free energy, replica overlaps, and overlap with the external field in the quadratic spherical SK model with a magnetic field. We identify several different behaviors for these quantities depending on the size of the magnetic field, confirming predictions by Fyodorov-Le Doussal and recent work of Baik, Collins-Wildman, Le Doussal and Wu.
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