# Spherical Spin Glass Model with External Field

@article{Baik2020SphericalSG, title={Spherical Spin Glass Model with External Field}, author={Jinho Baik and Elizabeth Collins-Woodfin and Pierre le Doussal and Hao Wu}, journal={arXiv: Disordered Systems and Neural Networks}, year={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 and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes to zero as the dimension of the spin variable grows. In particular, we consider overlaps with the…

## 10 Citations

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…

Mean Field Spin Glass Models under Weak External Field

- Physics
- 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…

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

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

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…

Equilibrium fluctuations in mean-field disordered models

- PhysicsPhysical Review E
- 2022

Mean-ﬁeld models of glasses that present a random ﬁrst order transition exhibit highly non-trivial ﬂuctuations. Building on previous studies that focused on the critical scaling regime, we here…

Fluctuations of the overlap at low temperature in the 2-spin spherical SK model

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

We describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order…

Generalised Gibbs Ensemble for spherically constrained harmonic models

- Mathematics
- 2022

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on…

Rank one HCIZ at high temperature: interpolating between classical and free convolutions

- MathematicsSciPost Physics
- 2022

We study the rank one Harish-Chandra-Itzykson-Zuber integral in the
limit where \frac{N\beta}{2} \to cNβ2→c, called the high-temperature regime and show that it
can be used to construct a promising…

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.

Inevitability of Red Queen evolution driven by organismic complexity and simple feedback via environmental modification

- Biology
- 2021

The simplest approximation of evolution, an almost-always clonal population evolving by small effect mutations under deterministic “adaptive” dynamics, is studied and organismic complexities, caricatured by a large number of constraints on the molecular-level phenotype, are shown to be sufficient to cause such Red Queen dynamics.

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

- MathematicsJournal of Mathematical Physics
- 2022

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 $\beta = 1 +\alpha \sqrt{ \log(N) } N^{-1/3}$.

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- 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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We prove the existence of a critical regime of fluctuation of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field. Such regime was conjectured in [2,12], and…

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We describe the fluctuations of the overlap between two replicas in the 2-spin spherical SK model about its limiting value in the low temperature phase. We show that the fluctuations are of order…

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In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated…