The Random-Cluster Model
Geoffrey R. Grimmett
ديسمبر 2006 · Grundlehren der mathematischen Wissenschaften الكتاب 333 · Springer Science & Business Media
كتاب إلكتروني
378
صفحة
reportلم يتم التحقّق من التقييمات والمراجعات. مزيد من المعلومات
معلومات عن هذا الكتاب الإلكتروني
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 bond percolation on the c 2 square lattice, and this was followed soon by Harry Kesten’s monograph on t- dimensionalpercolation. Percolationmovedintohigherdimensionsaround1986, and many of the mathematical issues of the day were resolved by 1989. Interest in the random-cluster model as a tool for studying the Ising/Potts models was rekindled around 1987.
نبذة عن المؤلف
PhD (Oxford 1974) under supervision of John Hammersley and Dominic Welsh. Member of the Mathematics Department of Bristol University (1976-1992), and subsequently appointed to the Professorship of Mathematics Statistics at Cambridge University. Author of around 100 articles and five books in probability and related fields, including Percolation (Springer 1999), Probability and Random Processes (with David Stirzaker, Oxford University Press 2001). Managing Editor of "Probability Theory and Related Fields", 2001-2005.
تقييم هذا الكتاب الإلكتروني
أخبرنا ما هو رأيك.
معلومات القراءة
الهواتف الذكية والأجهزة اللوحية
ينبغي تثبيت تطبيق كتب Google Play لنظام التشغيل Android وiPad/iPhone. يعمل هذا التطبيق على إجراء مزامنة تلقائية مع حسابك ويتيح لك القراءة أثناء الاتصال بالإنترنت أو بلا اتصال بالإنترنت أينما كنت.
أجهزة الكمبيوتر المحمول وأجهزة الكمبيوتر
يمكنك الاستماع إلى الكتب المسموعة التي تم شراؤها على Google Play باستخدام متصفح الويب على جهاز الكمبيوتر.
أجهزة القراءة الإلكترونية والأجهزة الأخرى
للقراءة على أجهزة الحبر الإلكتروني، مثل أجهزة القارئ الإلكتروني Kobo، عليك تنزيل ملف ونقله إلى جهازك. يُرجى اتّباع التعليمات المفصّلة في مركز المساعدة لتتمكّن من نقل الملفات إلى أجهزة القارئ الإلكتروني المتوافقة.
