Incoherent boundary conditions and metastates

TL;DR

This paper explores how incoherent boundary conditions influence phase transitions, especially in disordered systems like spin glasses, providing mathematical results for ferromagnetic models and discussing potential extensions.

Contribution

It offers new mathematical insights into the role of boundary conditions in phase transitions and introduces a metastate framework applicable to ferromagnetic models.

Findings

Mathematical results for ferromagnetic models with symmetry

Survey of boundary condition effects on phase transitions

Discussion of extending results to multiple pure states

Abstract

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.