Related papers: The Parisi formula completed
We establish both a Boltzmann-Gibbs principle and a Parisi formula for the limiting free energy of an abstract GREM (Generalized Random Energy Model) which provides an approximation of the TAP (Thouless-Anderson-Palmer) free energies…
These notes give an introduction to the physics of the infinite range version of the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model. In a first part, I motivate and introduce the Edwards--Anderson and…
For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…
We study mean-field spin glass models with general vector spins and convex covariance function. For those models, it is known that the limit of the free energy can be written as the supremum of a functional, this is the celebrated Parisi…
G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an elementary approach to the study of the Parisi functional…
We introduce a nonlinear, nonhierarchical generalization of Derrida's GREM and establish through a Sanov-type large deviation analysis both a Boltzmann-Gibbs principle as well as a Parisi formula for the limiting free energy. In line with…
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical…
We consider the spherical Sherrington-Kirkpatrick model of spin glass with sparse interaction, where the interactions between most of the pairs of the spin variables are possibly zero. With suitable normalization, we prove that the limiting…
The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…
We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time…
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,…
In this paper we consider a system of spins that consists of two configurations $\vsi^1,\vsi^2\in\Sigma_N=\{-1,+1\}^N$ with Gaussian Hamiltonians $H_N^1(\vsi^1)$ and $H_N^2(\vsi^2)$ correspondingly, and these configurations are coupled on…
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved…
We give a proof of the replica symmetric formula for the free energy of the Sherrington-Kirkpatrick model in high temperature which is based on the TAP formula. This is achieved by showing that the conditional annealed free energy equals…
Based on simple combinatorial arguments, we formulate a generalized cavity method where the Random Overlap Structure (ROSt) probability space of Aizenmann, Sims and Starr is obtained in a constructive way, and use it to give a simplified…
Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models,…
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 introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…
In [Physical Magazine, 35(3):593-601, 1977], Thouless, Anderson, and Palmer derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy…
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…