Translation invariant Gibbs states for the Ising model

• 成果类型: Article
• 署名作者: Bodineau, T
• 署名单位: Universite Paris Cite; Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-005-0457-0
• 发表日期: 2006
• 页码: 153-168
• 关键词: coexistence; percolation; crystal; phases; uniqueness; potts

摘要

We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases mu(+)(beta), mu(-)(beta) for any beta not equal beta(c). This implies that the average magnetization is continuous for beta > beta(c). Furthermore, combined with previous results on the slab percolation threshold [B2] this shows the validity of Pisztora's coarse graining [ Pi] up to the critical temperature.