Related papers: Parisi formula for balanced Potts spin glass
We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature.
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
We calculate the probability distribution of the overlap between a spin glass and a copy of itself in which the bonds are randomly perturbed in varying degrees. The overlap distribution is shown to go to a delta distribution in the…
We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of…
We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
In this paper we study the equilibrium statistical mechanical as well as the dynamical properties of a Sherrington and Kirkpatrick model in a multi-bath setting introduced in [4]. We show that the free energy per particle in the…
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…
We present a detailed analysis for the Langevin dynamics of a spherical spin-glass model (the spherical Sherrington-Kirkpatrick model). All the spins in the system are coupled by pairs via a random interaction matrix taken from the Gaussian…
Parisi demonstrated in 1979 that pairwise interactions exhibit a glass spin phase when there is disorder. While he discovered an equilibrium solution of the Sherrington-Kirkpatrick (SK) spin-glass model and we know it as a continuous phase…
We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and…
Numerical results up to 42nd order of replica symmetry breaking (RSB) are used to predict the singular structure of the SK spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model…
We develop further a recent dynamical replica theory to describe the dynamics of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution equations for macroscopic order parameters. We show how microscopic memory effects can be…
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 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…
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…
Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…