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Introduction to a Renormalisation Group Method pp 3–28Cite as

Spin Systems

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2242))

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.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK

    Roland Bauerschmidt

  2. Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada

    David C. Brydges & Gordon Slade

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  1. Roland Bauerschmidt
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  2. David C. Brydges
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Bauerschmidt, R., Brydges, D.C., Slade, G. (2019). Spin Systems. In: Introduction to a Renormalisation Group Method. Lecture Notes in Mathematics, vol 2242. Springer, Singapore. https://doi.org/10.1007/978-981-32-9593-3_1

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