Phase Separation for the Long Range One-dimensional Ising Model

Autor: Pierre Picco, Immacolata Merola, Marzio Cassandro
Přispěvatelé: INFN, Università dell'Aquila, Dipartimento di Ingegneria e Science dell'Informazione e Matematica (DISIM), Università degli Studi dell'Aquila (UNIVAQ), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), ANR-11-IDEX-0001,Amidex,INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE(2011), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Università degli Studi dell'Aquila = University of L'Aquila (UNIVAQ)
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Zdroj: Journal of Statistical Physics
Journal of Statistical Physics, Springer Verlag, 2016, 167 (2), pp.351-382. ⟨10.1007/s10955-017-1722-1⟩
Journal of Statistical Physics, 2016, 167 (2), pp.351-382. ⟨10.1007/s10955-017-1722-1⟩
ISSN: 0022-4715
1572-9613
DOI: 10.1007/s10955-017-1722-1⟩
Popis: Dedicated to the memory of Enza Orlandi.; International audience; 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.
Databáze: OpenAIRE
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