Phase Separation for the Long Range One-dimensional Ising Model - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Phase Separation for the Long Range One-dimensional Ising Model

Résumé

We consider the phase separation problem for the one--dimensional ferromagnetic Ising model with long--range two--body interaction, $J(n)=n^{-2+\a}$ where $n\in \N$ denotes the distance of the two spins and $ \alpha \in ]0,\a_+[$ with $\a_+=(\log 3)/(\log 2) -1$. We prove that given $m\in ]-1,+1[$, if the temperature is small enough, then typical configuration for the $\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization of the order $m$ are made of a single interval that occupy almost a proportion $\frac{1}{2}(1-\frac{m}{m_\b})$ of the volume with the minus phase inside and the rest of the volume is the plus phase, here $m_\b>0 $ is the spontaneous magnetization.
Fichier principal
Vignette du fichier
1611.02310.pdf (324.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01583368 , version 1 (05-10-2023)

Identifiants

Citer

Marzio Cassandro, Immacolata Merola, Pierre Picco. Phase Separation for the Long Range One-dimensional Ising Model. 2016. ⟨hal-01583368⟩
91 Consultations
4 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More