EXISTENCE OF GRADIENT GIBBS MEASURES ON REGULAR TREES WHICH ARE NOT TRANSLATION INVARIANT

• 成果类型: Article
• 署名作者: Henning, Florian; Kuelske, Christof
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1883
• 发表日期: 2023
• 页码: 3010-3038
• 关键词: ising-model; coexistence; phases; FIELDS; STATES

摘要

We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain are delocalized. The construction we provide for them starts from a two-layer hidden Markov model representation in a setup which is not invari-ant under tree-automorphisms, involving internal q-spin models. The proofs of existence and lack of translation invariance of infinite-volume gradient states are based on properties of the local pseudo-unstable manifold of the corresponding discrete dynamical systems of these internal models, around the free state, at large q.