# Extended variational principle for the Sherrington-Kirkpatrick spin-glass model

@article{Aizenman2003ExtendedVP, title={Extended variational principle for the Sherrington-Kirkpatrick spin-glass model}, author={Michael Aizenman and Robert Sims and Shannon L. Starr}, journal={Physical Review B}, year={2003}, volume={68}, pages={214403} }

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherringtun-Kirkpatrick (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 broader variational principle, in which the lower bound as well as the actual value are expressed through an optimization procedure for which ultrametric/hierarchal structures form only a subset of the variational class. The validity of…

## 155 Citations

A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models

- Mathematics
- 2006

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the…

The free energy in a multi-species Sherrington-Kirkpatrick model

- Mathematics
- 2013

The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free…

MEAN-FIELD SPIN GLASS MODELS FROM THE CAVITY-ROST PERSPECTIVE

- Mathematics
- 2006

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with hi ghly diversified collections of competing low energy states. The…

Interpolation and Comparison Methods in the Mean Field Spin Glass Model

- Mathematics
- 2014

We give a short overview of the recent rigorous mathematical methods developed for the study of complex disordered systems, in particular spin glasses in the mean field Sherrington-Kirkpatrick…

Free energy in the Potts spin glass

- Mathematics
- 2015

We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are…

Free Energy Expansion in Quasi Stationary ROSt

- Computer Science
- 2007

This paper derives recursively an expression for the free energy of the Sherrington-Kirkpatrick model in the framework of Random Overlap Structures (ROSt) recently introduced by Aizenman and coworkers via the infinite irreducible overlap correlation functions, which act globally as a sort of order parameter of the theory.

Random Multi-Overlap Structures and Cavity Fields in Diluted Spin Glasses

- Physics
- 2004

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by Aizenman, Sims and Starr for non-diluted spin glasses. We use such concept to find…

Estimation in spin glasses: A first step

- Computer Science
- 2006

Under bare minimal conditions, it is established the $\sqrt{N}$-consistency of the maximum pseudolikelihood estimate of the natural parameter in this family, even at critical temperatures.

Mean field spin glasses treated with PDE techniques

- Physics
- 2013

Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the…

Structural Properties of the Disordered Spherical and Other Mean Field Spin Models

- Physics
- 2007

We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorization…