https://hal-univ-paris.archives-ouvertes.fr/hal-03674858Foini, LauraLauraFoiniIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueKurchan, JorgeJorgeKurchanLPENS - Laboratoire de physique de l'ENS - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris CitéAnnealed averages in spin and matrix modelsHAL CCSD2022[PHYS] Physics [physics]Université Paris Cité, Equipe HAL2022-05-21 15:19:302022-08-05 11:58:362022-05-21 15:19:30enJournal articles10.21468/SciPostPhys.12.3.0801A disordered system is denominated `annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite (`quenched') situation when disorder is fixed, is the one relevant for physical spin-glasses, and has received vastly more attention. Other problems however are more natural in the annealed situation: in this work we discuss examples where annealed averages are interesting, in the context of matrix models. We first discuss how in practice, when system and disorder adapt together, annealed systems develop `planted' solutions spontaneously, as the ones found in the study of inference problems. In the second part, we study the probability distribution of elements of a matrix derived from a rotationally invariant (not necessarily Gaussian) ensemble, a problem that maps into the annealed average of a spin glass model.