From inherent structures to pure states: Some simple remarks and examples
Laboratoire de Physique Théorique de l'Ecole Normale
Supérieure Unité Mixte de Recherche du Centre National de la
Recherche Scientifique et de l'Ecole Normale Supérieure.
24 rue Lhomond, 75231 Paris cedex 05, France
Accepted: 16 February 2000
The notions of pure states and inherent structures, i.e. stable configurations against 1-spin flip are discussed. We explain why these different concepts accidentally coincide in mean-field models with infinite connectivity and present an exactly solvable one-dimensional model where they do not. At zero temperature pure states are to some extent related to k-spin flip stable configurations with after the thermodynamical limit has been taken. This relationship is supported by an explicit analysis of the TAP equations and calculation of the number of pure states and k-spin flips stable configurations in a mean-field model with finite couplings. Finally, we discuss the relevance of the concepts of pure states and inherent structures in finite-dimensional glassy systems.
PACS: 05.20-y – Classical statistical mechanics / 64.70.Pf – Glass transitions / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, 2000