Open Access
VOL. 48 | 2006 Incoherent boundary conditions and metastates
Aernout C. D. van Enter, Karel Netočný, Hendrikjan G. Schaap

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 144-153 (2006) DOI: 10.1214/074921706000000176


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1125.82016
MathSciNet: MR2306196

Digital Object Identifier: 10.1214/074921706000000176

Primary: 82B20 , 82B44
Secondary: 60F99 , 60K35

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

Rights: Copyright © 2006, Institute of Mathematical Statistics

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