Related papers: Bounds for diluted mean-fields spin glass models
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
We compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive…
We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the…
We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids.…
We consider a finite range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance $\gamma^{-1}$. We show that, under mild assumptions on the interaction potential, the…
connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
We present two rigorous results on the Sherrington-Kirkpatrick mean field model for spin glasses, proven by elementary methods, based on properties of fluctuations, with respect to the external quenched noise, of the thermodynamic variables…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…
We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By…
We show that Glauber dynamics for $ p$-spin glass mixes exponentially slowly at inverse temperatures larger than a constant times $ \ln (p)/p $ for large enough $ p $. This is done by analyzing the energy landscape using Gaussian…
Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type…
We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions, well…
We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed $p$-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the…
We study the free energy for pure and mixed spherical $p$-spin models with i.i.d.\ disorder. In the mixed case, each $p$-interaction layer is assumed either to have regularly varying tails with exponent $\alpha_p$ or to satisfy a finite…
In this paper we study two non-mean-field spin models built on a hierarchical lattice: The hierarchical Edward-Anderson model (HEA) of a spin glass, and Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence…
In Phys. Rev. Lett. 110, 219701 (2013) [arXiv:1211.0843] Billoire et al. criticize the conclusions of our Letter [Phys. Rev. Lett. 109, 177204 (2012), arxiv:1206.0783]. They argue that considering the Edwards-Anderson and…
We show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed…
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…