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

@article{Aizenman2006MEANFIELDSG, title={MEAN-FIELD SPIN GLASS MODELS FROM THE CAVITY-ROST PERSPECTIVE}, author={Michael Aizenman and Robert Sims and Shannon L. Starr}, journal={arXiv: Mathematical Physics}, year={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 goal of this summary is to present some of the ideas which have emerged in the mathematical study of its free energy. In particular, we high- light the perspective of the cavity dynamics, and the relate d variational principle. These are expressed in terms of Random Overlap Structures (ROSt), which…

## 48 Citations

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…

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.

Spin glass polynomial identities from entropic constraints

- Mathematics
- 2012

The core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field…

The Aizenman-Sims-Starr scheme for the SK model with multidimensional spins

- Mathematics
- 2007

The non-hierarchical correlation structure of the Sherrington-Kirkpatrick (SK) model with multidimensional (e.g. Heisenberg) spins is studied at the level of the logarithmic asymptotic of the…

Stability properties and probability distributions of multi-overlaps in dilute spin glasses

- Economics
- 2006

We prove that the Aizenman–Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit for…

Overlap fluctuations from the Boltzmann random overlap structure

- Physics
- 2006

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…

O ct 2 01 2 Spin glass polynomial identities from entropic constraints

- Mathematics
- 2012

The core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field…

Competing Particle Systems and the Ghirlanda

- Mathematics
- 2008

Competing particle systems are point processes on the real line whose configurations X can be ordered decreasingly and evolve by increments which are functions of correlated Gaussian variables. The…

0 A ug 2 00 6 Overlap Fluctuations from Random Overlap Structures

- Physics
- 2008

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…

M ay 2 00 8 Fluctuations of the partition function in the GREM with external field

- Mathematics
- 2008

We study Derrida’s generalized random energy model in the pr esence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit…

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