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Universality of Chaos and Ultrametricity in Mixed p ‐Spin Models
Author(s) -
Auffinger Antonio,
Chen WeiKuo
Publication year - 2016
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21617
Subject(s) - universality (dynamical systems) , spin glass , statistical physics , gaussian , mathematics , ising model , mean field theory , renormalization group , spin model , ising spin , random field , perturbation (astronomy) , mathematical physics , condensed matter physics , physics , quantum mechanics , statistics
We prove disorder universality of chaos phenomena and ultrametricity in the mixed p ‐spin model under mild moment assumptions on the environment. This establishes the longstanding belief among physicists that the solution of mean‐field models with Gaussian disorder also holds for different environments. Our results extend to the mixed p ‐spin model as well as to different spin glass models. These include universality of quenched disorder chaos in the Edwards‐Anderson (EA) model and quenched concentration for the magnetization in both EA and mixed p ‐spin models under non‐Gaussian environments. In addition, we show quenched self‐averaging for the overlap in the random field Ising model under small perturbation of the external field.© 2015 Wiley Periodicals, Inc.