Related papers: Universality In Sherrington-Kirkpatrick's Spin Gla…
We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising…
The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a…
We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach…
In this work, we revisit the shear-free conjecture of general relativity and show the violation of the well-known shear-free condition for perfect-fluid spacetimes. It had been shown in previous investigations that, in the general…
We suggest a possible approach to proving the M\'ezard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we…
The spherical Sherrington-Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy-Widom at low temperature.…
We show through a simple example that perturbations of the Hamiltonian of a spin glass which cannot be detected at the level of the free energy can completely alter the behavior of the overlap. In particular, perturbations of order O(log…
We study numerically the out of equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low dimensional models.…
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the…
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within…
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…
This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic…
We review the long-time off-equilibrium dynamical behaviour of two representative mean-field spin-glass models, namely the $p$-spin spherical and the Sherrington-Kirkpatrick models. We show how both models capture aging phenomena but with…
We argue that the lower bound to the barrier energy to flip an up/down spin domain embedded in a down/up spin environment for Ising spin glass is independent of the size of the system. The argument shows the existence of at least one…
This paper studies spin glass to paramagnetic transition in the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J$ and inverse temperature $\beta$. The disorder of the system is…
In this note, we consider the multi-species Sherrington-Kirkpatrick spin glass model at its conjectured critical temperature, and we show that, when the variance profile matrix $\Delta^2$ is positive semi-definite, the variance of the free…
We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of…
We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here…
We present a detailed study of simple `tree' models for off equilibrium dynamics and aging in glassy systems. The simplest tree describes the landscape of a random energy model, whereas multifurcating trees occur in the solution of the…