Ising models and multiresolution quad-trees
Ising models and multiresolution quad-trees
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Ising 模型和多分辨率四叉树
DOI：
10.1239/aap/1046366101
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发表时间：
2003
影响因子：
1.2
通讯作者：
R. Wilson
中科院分区：
文献类型：
--
作者：
W. Kendall;R. Wilson
我们研究了多分辨率图像分析中使用的四叉树的推广定义的渗流和伊辛模型。这些可以被看作是树，其中每个母顶点有2个子顶点，并且子顶点在d维欧几里德配置中连接在一起。保留概率和相互作用强度根据相关的债券是母亲和女儿之间或邻居之间的不同。边界的建立，定位相变和共存相的渗流模型的存在。结果扩展到相应的伊辛模型使用Fortuin-Kasteleyn随机集群表示。
We study percolation and Ising models defined on generalizations of quad-trees used in multiresolution image analysis. These can be viewed as trees for which each mother vertex has 2 d daughter vertices, and for which daughter vertices are linked together in d-dimensional Euclidean configurations. Retention probabilities and interaction strengths differ according to whether the relevant bond is between mother and daughter or between neighbours. Bounds are established which locate phase transitions and show the existence of a coexistence phase for the percolation model. Results are extended to the corresponding Ising model using the Fortuin-Kasteleyn random-cluster representation.