Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fluctuations of the 2-spin SSK model with magnetic field

Benjamin Landon, Philippe Sosoe

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.

Fluctuations of the 2-spin SSK model with magnetic field

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.

Paper Structure

This paper contains 56 sections, 63 theorems, 460 equations, 1 table.

Table of Contents

  1. Introduction
  2. Model with zero magnetic field.
  3. Model with magnetic field.
  4. Organization of paper
  5. Acknowledgements.
  6. Main results and notation
  7. Notation
  8. High temperature or slowly decaying magnetic field (Gaussian regime)
  9. Free energy.
  10. Overlap with external field.
  11. Overlap between replicas.
  12. Low temperature and intermediate magnetic field
  13. Free energy.
  14. Overlap with external field.
  15. Overlap between two replicas.
  16. ...and 41 more sections

Key Result

Theorem 2.1

We have the following in various parameter regimes:

Theorems & Definitions (64)

  • Theorem 2.1: Free energy fluctuations
  • Theorem 2.2: Quenched external field overlap fluctuations
  • Theorem 2.3: Quenched replica overlap fluctuations
  • Theorem 2.4: Free energy expansion
  • Theorem 2.5: Free energy fluctuations
  • Theorem 2.6: Quenched external field overlap fluctuations
  • Theorem 2.7: Quenched external field overlap expectation
  • Theorem 2.8: Quenched replica overlap fluctuations
  • Theorem 2.9: Free energy fluctuations
  • Theorem 2.10: Overlaps measure
  • ...and 54 more