From inherent structures to pure states: some simple remarks and examples

Details From inherent structures to pure states: some simple remarks and examples From inherent structures to pure states: some simple remarks and examples

1999-12-03

arxiv.org/abs/cond-mat/9912061v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 revtex pages + 1 eps figure. To appear in Europhys.Lett

Scientific paper

10.1209/epl/i2000-00248-2

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 unidimensional model where they do not. At zero temperature pure states are to some extent related to k-spin flip stable configurations with k going to infinity 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.

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