Abstract
Random-walk expansions have played a key role in recent advances in our understanding of critical phenomena in statistical mechanics and of the continuum limit in quantum field theory. These advances include the proof of triviality of the continuum limit and mean-field critical behavior for φ 4 and Ising models in dimensions d > 4 [5, 15, 8, 12, 213, 90, 28, 292, 223], and an extremely simple construction of continuum φ 4 quantum field theories in dimensions d < 4 [97, 96, 74, 75, 292]. Our goal in Parts II and III is to present several random-walk expansions from a unified point of view, and to explain the physical results which can (and cannot) be derived from them.
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© 1992 Springer-Verlag Berlin Heidelberg
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Fernández, R., Fröhlich, J., Sokal, A.D. (1992). Introduction. In: Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02866-7_8
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DOI: https://doi.org/10.1007/978-3-662-02866-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02868-1
Online ISBN: 978-3-662-02866-7
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