Related papers: Parisi PDE and convexity for vector spins
The Parisi formula for the free energy is among the crown jewels in the theory of spin glasses. We present a simpler proof of the lower bound in the case of the spherical mean-field model. Our method follows the TAP approach developed…
We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…
The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme…
We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order…
We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscillate as the system size increases. While the extensive part…
This is the first of a series of three papers about the Elastic Manifold model. This classical model proposes a rich picture due to the competition between the inherent disorder and the smoothing effect of elasticity. In this paper, we…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…
The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi…
In 1979, G. Parisi predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model and described the role played by its minimizer. This formula was verified in the seminal work of…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We study the free energy of mixed $p$-spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove that this free energy converges to the…
We investigate the structure of Parisi measures, the functional order parameters of mixed p-spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First,…
We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature…
The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…
We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy…
We study the problem of algorithmically optimizing the Hamiltonian $H_N$ of a spherical or Ising mixed $p$-spin glass. The maximum asymptotic value $\mathsf{OPT}$ of $H_N/N$ is characterized by a variational principle known as the Parisi…
This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers…