The weak limit of Ising models on locally tree-like graphs
The weak limit of Ising models on locally tree-like graphs
复制标题
Ising 模型在局部树状图上的弱极限
DOI：
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发表时间：
2009
影响因子：
2
通讯作者：
A. Sly
中科院分区：
文献类型：
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作者：
A. Montanari;Elchanan Mossel;A. Sly
我们在局部收敛到 k 正则树的图 Gn 序列上考虑具有逆温度 β 且没有外场的 Ising 模型。我们表明，对于此类图，Ising 测度局部弱收敛到具有逆温度 β 的 k-正则树上具有 + 边界条件和 - 边界条件的 Ising 模型的对称混合。在图 Gn 是扩展器的情况下，我们通过显示以正磁化强度（自旋之和）为条件的 Ising 测量值与树上的 + 测量值的收敛，得出更详细的理解。
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs Gn are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree.