@inbook{8e475c962d25471b8d1ca292465618e8,

title = "Spin Systems",

abstract = "We provide an introduction to the theory of critical phenomena and discusses several of the models which serve as guiding examples. The Ising and multi-component |φ|4 spin models are introduced and motivated, with emphasis on their critical behaviour. The theory of the mean-field model is developed in a self-contained manner. The Gaussian free field is introduced and its relation to simple random walk is explained. The notion of universality is discussed. Recent results for the critical behaviour of the |φ|4 model are summarised, including the existence of logarithmic corrections to mean-field critical exponents in dimension d = 4.",

keywords = "Critical exponent, Critical phenomena, Ising model, Mean-field model, |φ| model",

author = "Roland Bauerschmidt and Brydges, {David C.} and Gordon Slade",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Singapore Pte Ltd.",

year = "2019",

doi = "10.1007/978-981-32-9593-3_1",

language = "English (US)",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "3--28",

booktitle = "Lecture Notes in Mathematics",

}