THOULESS-ANDERSON-PALMER EQUATIONS FOR GENERIC p-SPIN GLASSES

• 成果类型: Article
• 署名作者: Auffinger, Antonio; Jagannath, Aukosh
• 署名单位: Northwestern University; Harvard University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1307
• 发表日期: 2019
• 页码: 2230-2256
• 关键词: ultrametricity

摘要

We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, <.>(N), into a mixture of conditional laws, <.>(alpha,N). We show that the TAP equations hold for the spin at any site with respect to <.>(alpha,N) simultaneously for all alpha. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.