| 书目名称 | The Random-Cluster Model | | 编辑 | Geoffrey R. Grimmett | | 视频video | | | 概述 | Sequel to G. Grimmett‘s famous and influential book on Percolation (Grundlehren der mathematischen Wissenschaften 321).Author is leader in the field, and known as masterly expositor.Includes some hist | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | Therandom-clustermodelwasinventedbyCees[Kees]FortuinandPietKasteleyn around 1969 as a uni?cation of percolation, Ising, and Potts models, and as an extrapolation of electrical networks. Their original motivation was to harmonize the series and parallel laws satis?ed by such systems. In so doing, they initiated a study in stochastic geometry which has exhibited beautiful structure in its own right, and which has become a central tool in the pursuit of one of the oldest challenges of classical statistical mechanics, namely to model and analyse the ferromagnet and especially its phase transition. The importance of the model for probability and statistical mechanics was not fully recognized until the late 1980s. There are two reasons for this period of dormancy. Although the early publications of 1969–1972 contained many of the basic properties of the model, the emphasis placed there upon combinatorial aspects may have obscured its potential for applications. In addition, many of the geometrical arguments necessary for studying the model were not known prior to 1980, but were developed during the ‘decade of percolation’ that began 1 then. In 1980 was published the proof that p = for bo | | 出版日期 | Book 2006 | | 关键词 | Ising model; Potts model; Random-cluster model; ferromagnetism; geometry; percolation | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-32891-9 | | isbn_softcover | 978-3-642-06943-7 | | isbn_ebook | 978-3-540-32891-9Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 2006 |
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发表于 2025-3-21 17:41:47
