Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)

**Résumé:** We consider the problem of temperature dependence
of the Gibbs states in
two spin-glass models: Derrida's Random
Energy Model and its analogue, where
the random variables in the Hamiltonian are replaced by independent
standard Brownian motions.
For both of them we compute in the thermodynamic limit
the overlap distribution
$ \sum_{i=1}^{N}\s_i\s'_i/N\in [0,1]$
of two spin configurations $\s$, $\s'$
under the product of two
Gibbs measures, which are taken at temperatures
$T, T'$ respectively.
If $T\ne T'$ are fixed, then at low temperature phase
the results are different for these models:
for the first one this distribution is
$D_0\delta_0+D_1\delta_2$, with random
weights $D_0$, $D_1$, while for the second one it is
$\delta_0$. We compute consequently the overlap
distribution for the second model whenever $T-T'\to 0$
at different speeds as $N\to \infty$.

**Mots Clés:** *Gaussian processes ; spin-glasses ; random energy model ; overlap ; Poisson point processes*

**Date:** 2002-05-30

**Prépublication numéro:** *PMA-734*

**Pdf file : **PMA-734.pdf