• Corpus ID: 201106529

Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field

  title={Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field},
  author={Pax Kivimae},
  journal={arXiv: Probability},
  • Pax Kivimae
  • Published 20 August 2019
  • Physics
  • arXiv: Probability
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 occurs with external field strength $h=O(N^{-1/6})$. Additional results are proven for $\beta$-analogues of the spherical Sherrington-Kirkpatrick model, and models with a Curie-Weiss term. In particular, we introduce a three-parameter family $TW_{\beta,w}^h$ (generalizing the two-parameter family of… 

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

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

Overlaps of a spherical spin glass model with microscopic external field

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

Generalised Gibbs Ensemble for spherically constrained harmonic models

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

Fluctuations of the 2-spin SSK model with magnetic field

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

Optimization landscape in the simplest constrained random least-square problem

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.

Spherical Spin Glass Model with External Field

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 Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction

We consider a spherical spin system with pure 2-spin spherical Sherrington–Kirkpatrick Hamiltonian with ferromagnetic Curie–Weiss interaction. The system shows a two-dimensional phase transition with

On the overlap in the multiple spherical SK models

In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the

Parisi Formula, Disorder Chaos and Fluctuation for the Ground State Energy in the Spherical Mixed p-Spin Models

We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for

Beta ensembles, stochastic Airy spectrum, and a diffusion

We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schroedinger operator -d^2/dx^2 + x +

The sphericalp-spin interaction spin glass model: the statics

The static properties of the sphericalp-spin interaction spin glass model are calculated using the replica method. It is shown that within the Parisi scheme the most general solution is the one-step

Asymptotic correlations for Gaussian and Wishart matrices with external source

We consider ensembles of Gaussian (Hermite) and Wishart (Laguerre) $N\times N$ hermitian matrices. We study the effect of finite rank perturbations of these ensembles by a source term. The rank $r$

Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N−1)-dimensional sphere is one of the simplest, yet paradigmatic problems in

Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let Tn be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that

Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials

We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals \((a,b) \subseteq \mathbb{R}\) associated with rather general differential expressions of

Large gaps between random eigenvalues.

We show that in the point process limit of the bulk eigenvalues of β-ensembles of random matrices, the probability of having no eigenvalue in a fixed interval of size λ is given by as λ → ∞, where (κ