# Fluctuations of the 2-spin SSK model with magnetic field

@article{Landon2020FluctuationsOT, title={Fluctuations of the 2-spin SSK model with magnetic field}, author={Benjamin Landon and Philippe Sosoe}, journal={arXiv: Probability}, year={2020} }

We analyze the fluctuations of the free energy, replica overlaps, and overlap with the magnetic fields in the quadratic spherial SK model with a vanishing 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.

## 8 Citations

Spherical Spin Glass Model with External Field

- Physics
- 2020

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model…

Fluctuations of the free energy of the mixed $p$-spin mean field spin glass model

- Physics
- 2021

The Sherrington-Kirkpatrick [SK75] model and its variants [Der80; GM84; Tal00] are important models of disordered magnetic systems and paradigmatic examples in the theory of complex systems [MPV87;…

Free energy fluctuations of the two-spin spherical SK model at critical temperature

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The fluctuations of the free energy of the $2-spin spherical Sherrington-Kirkpatrick model at critical temperature are investigated and it is proved the existence of a critical window on the scale of $\beta = 1 +\alpha \sqrt{ \log(N) } N^{-1/3}$.

Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington–Kirkpatrick model

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We revisit the gradient descent dynamics of the spherical Sherrington–Kirkpatrick (p = 2) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the…

Mean Field Spin Glass Models under Weak External Field

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- 2021

. We study the ﬂuctuation and limiting distribution of free energy in mean-ﬁeld Ising spin glass models under weak external ﬁelds. We prove that at high temperature, there are three sub-regimes…

Spherical Sherrington-Kirkpatrick model for deformed Wigner matrix with fast decaying edges

- Mathematics
- 2021

Consider the deformed Wigner matrix W+λV where W is an N×N random real symmetric matrix, λ > 0 is a constant and V is an N × N random diagonal matrix with iid real-valued entries. Assume that the…

Optimization landscape in the simplest constrained random least-square problem

- Mathematics, Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2022

The compatibility threshold α c < 1 is found which is the value of α beyond which a large random linear system on the N-sphere becomes typically incompatible.

Overlaps of a spherical spin glass model with microscopic external field

- PhysicsElectronic Journal of Probability
- 2021

We examine the behavior of the 2-spin spherical Sherrington-Kirkpatrick model with an external ﬁeld by analyzing the overlap of a spin with the external ﬁeld. Previ-ous research has noted that, at…

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