# Replica Theory and Spin Glasses

@article{Morone2014ReplicaTA, title={Replica Theory and Spin Glasses}, author={F. Morone and Francesco Caltagirone and Elizabeth Harrison and Giorgio Parisi}, journal={arXiv: Statistical Mechanics}, year={2014} }

These are notes from the lectures of Giorgio Parisi given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithm", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC and ENS Paris, Federico Ricci-Tersenghi from "La Sapienza" Roma, Lenka Zdeborov\'a from CEA Saclay and CNRS, and Riccardo Zecchina from Politecnico Torino. The first lecture…

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## References

SHOWING 1-10 OF 12 REFERENCES

### SPIN GLASS MODELS FROM THE POINT OF VIEW OF SPIN DISTRIBUTIONS

- Mathematics
- 2013

In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous–Hoover representation encoded by a function σ :…

### On the Stability of the Quenched State in Mean-Field Spin-Glass Models

- Mathematics
- 1998

While the Gibbs states of spin-glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying “quenched state.”…

### Spin-Glass Stochastic Stability: a Rigorous Proof

- Mathematics
- 2005

Abstract.We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spinglass quenched state. We show that…

### Spin Glass Theory and Beyond

- Physics
- 1987

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…

### The Parisi Formula has a Unique Minimizer

- Mathematics
- 2015

In 1979, Parisi (Phys Rev Lett 43:1754–1756, 1979) predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington–Kirkpatrick model, and described the role played…

### Communications in Mathematical Physics

- Mathematics

VoI.293:R.A.DeVore: The Approximation of Continous Functions by Positive Linear Operators VIII, 289 pages. 1972 DM 24,-; US $7.70 Vol.294: Stability of Stochastic Dynamical Systems Proceedings of the…

### Annals of Mathematics

- Mathematics
- 1889

ing from the embeddability relation between order types, define a quasi-order to be a reflexive, transitive relation. Throughout this paper, the letters Q and R will range over quasi-ordered sets and…

### A mathematical reformulation of Derrida's REM and GREM

- Physics
- 1987

The large system limit of the Random Energy Model (REM) and generalized Random Energy Model (GREM) of Derrida is investigated, and found to be universal. This permits systematic calculations of…

### Commun

- Math. Phys., 230:71–79
- 2002