Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
复制标题
DOI：
10.1007/bf02199113
复制
发表时间：
1996-03
影响因子：
1.6
通讯作者：
J. Salas;A. Sokal
中科院分区：
文献类型：
--
作者：
J. Salas;A. Sokal
我们证明，当q>2r时，最大配位数晶格上的q态Potts反铁磁体在所有温度（包括零温度）下均匀地表现出相关指数衰减。我们还证明了几个二维格子的更好的界限：方形格子（q≥7 时指数衰减）、三角形格子（q≥11）、六角形格子（q≥4）和 Kagomé 格子（q≥6）。证明基于 Dobrushin 唯一性定理。
We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberrexhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq≥7), triangular lattice (q≥11), hexagonal lattice (q≥4), and Kagomé lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.