Institute of Mathematical Statistics Lecture Notes - Monograph Series

Incoherent boundary conditions and metastates

Aernout C. D. van Enter, Karel Netočný, and Hendrikjan G. Schaap

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In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses. For the moment our mathematical results only apply to ferromagnetic models which have an exact symmetry between low-temperature phases. We give a survey of these results and discuss possibilities to extend them to some situations where many pure states can coexist. An idea of the proofs as well as the reformulation of our results in the language of Newman-Stein metastates are also presented.

Chapter information

Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 144-153

First available in Project Euclid: 28 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F99: None of the above, but in this section

chaotic size dependence metastates random boundary conditions Ising model local limit behaviour

Copyright © 2006, Institute of Mathematical Statistics


van Enter, Aernout C. D.; Netočný, Karel; Schaap, Hendrikjan G. Incoherent boundary conditions and metastates. Dynamics & Stochastics, 144--153, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000176.

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