Incoherent boundary conditions and metastates

Details Incoherent boundary conditions and metastates Incoherent boundary conditions and metastates

2005-02-08

arxiv.org/abs/math-ph/0502031v2

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 144-153

Physics

Mathematical Physics

Published at http://dx.doi.org/10.1214/074921706000000176 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

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.

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