An Extended Variational Principle for the SK Spin-Glass Model

@inproceedings{Aizenman2003AnEV,
  title={An Extended Variational Principle for the SK Spin-Glass Model},
  author={Michael Aizenman and Robert Sims and Shannon L. Starr},
  year={2003}
}
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 broader variational principle, in which the lower bound, as well as the actual value, are expressed through an optimization procedure for which ultrametic/hierarchal structures form only a subset of the variational class. The validity of Parisi’s ansatz for the… 

The Aizenman-Sims-Starr and Guerras schemes for the SK model with multidimensional spins

We prove upper and lower bounds on the free energy of the Sherrington-Kirkpatrick model with multidimensional spins in terms of variational inequalities. The bounds are based on a multidimensional

A note on the free energy of the coupled system in the Sherrington-Kirkpatrick model

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,

Notes on the Polynomial Identities in Random Overlap Structures

In these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of

A Short Course on Mean Field Spin Glasses

We give a brief introduction to the theory of mean field models of spin glasses. This includes a concise presentation of the Random Energy model and the Generalized Random Energy model and the

M ay 2 00 4 Random Multi-Overlap Structures and Cavity Fields in Diluted Spin Glasses

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by M. Aizenman R. Sims and S. L. Starr for non-diluted spin glasses. We use such method

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

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

Overlap fluctuations from the Boltzmann random overlap structure

We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Overlap Structure (ROSt). The concept of ROSt has been introduced

Random multi-overlap structures for optimization problems

TLDR
A generalized bound and an extended variational principle for the free energy per site in the thermodynamic limit are proved and a trial function implementing ultrametric breaking of replica symmetry is exhibited.

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

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

FREE ENERGY IN THE POTTS SPIN GLASS1 BY DMITRY PANCHENKO

  • 2018
...

References

SHOWING 1-10 OF 12 REFERENCES

Comm

  • Math. Phys. 233, 1
  • 2003

Spin Glass Theory and Beyond

This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular

A: Math

  • Gen. 13, 1101
  • 1980

Comm

  • Math. Phys. 230, 71
  • 2002

Spin Glasses: A Challenge for Mathematicians

Part of my standard advice to graduate students seeking a career in mathematics research is that, sometime during their second or third year, they should spend six months getting to grips with the

Comm

  • Math. Phys. 112, 3
  • 1987

Phys

  • 62, 1
  • 1991

Comm

  • Math. Phys. 236, 55
  • 2003

Comm

  • Math. Phys. 112, 553
  • 1987

Phys

  • Rev. B 24, 2613
  • 1981