无界自旋系统N点关联的聚类界
Clustering Bounds on N-Point Correlations for Unbounded Spin Systems
摘要：
我们证明了截断相关性的聚类估计，即，晶格上无界自旋系统的累积量。我们提供了一个统一的治疗，基于集群扩展技术，四个不同的制度：大质量，小网站之间的相互作用，大自我相互作用，以及更微妙的小自我相互作用或“低温”制度。在后一种制度的集群估计是需要的玻色子的情况下，最近得到的结果Lukkarinen和Spohn的严格控制量子流体的动力学尺度。
英文摘要：
We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small interaction between sites, large self-interaction, as well as the more delicate small self-interaction or `low temperature' regime. A clustering estimate in the latter regime is needed for the Bosonic case of the recent result obtained by Lukkarinen and Spohn on the rigorous control on kinetic scales of quantum fluids.
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