# Extreme Value Statistics Distributions in Spin Glasses

Abstract : We study the probability distribution of the pseudo-critical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick (SK) and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudo-critical point and and the Extreme Value Statistics of random variables. For the SK model, both with Gaussian and binary couplings, the distribution of the pseudo-critical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like $Fe_{0.5} Mn_{0.5} Ti O_3$ or $Eu_{0.5} Ba_{0.5} Mn O_3$, its pseudo-critical point distribution should be a priori experimentally accessible.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00658625
Contributor : Claudine Le Vaou <>
Submitted on : Tuesday, January 10, 2012 - 5:24:36 PM
Last modification on : Wednesday, October 14, 2020 - 4:08:41 AM

### Identifiers

• HAL Id : hal-00658625, version 1
• ARXIV : 1107.1795

### Citation

Michele Castellana, Aurelien Decelle, Elia Zarinelli. Extreme Value Statistics Distributions in Spin Glasses. Physical Review Letters, American Physical Society, 2011, 107, pp.275701. ⟨hal-00658625⟩

Record views