Journal ArticleDOI
On the triviality of λϕd4 theories and the approach to the critical point in d(−) > 4 dimensions
TLDR
In this paper, it was shown that one-and two-component λ|ϕ|4 theories and non-linear σ-models in five or more dimensions approach free or generalized free fields in the continuum (scaling) limit.About:
This article is published in Nuclear Physics.The article was published on 1982-02-01. It has received 504 citations till now. The article focuses on the topics: Scalar field & Critical exponent.read more
Citations
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Renormalization and effective lagrangians
TL;DR: In this paper, a renormalization group equation for a four-dimensional λo4 theory with a momentum cutoff was derived, and the cutoff dependence of the effective lagrangian was analyzed.
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A theory of regularity structures
TL;DR: In this paper, the authors introduce a regularity structure for describing functions and distributions via a kind of "jet" or local Taylor expansion around each point, which allows to describe the local behaviour not only of functions but also of large classes of distributions.
Journal ArticleDOI
A theory of regularity structures
TL;DR: In this article, a regularity structure is introduced to describe functions and distributions via a kind of "jet" or local Taylor expansion around each point, which allows to describe the local behaviour not only of functions but also of large classes of distributions.
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Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
TL;DR: In this article, the conceptual foundations of the renormalization-group (RG) formalism are considered and rigorous theorems on the regularity properties and possible pathologies of the RG map are presented.
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Geometric analysis of φ4 fields and Ising models. Parts I and II
TL;DR: In this article, it was shown that the φ4 Euclidean field theory with a lattice cut-off is inevitably free in the single phase regime in ind>4 dimensions, and that the critical behavior in Ising models is in exact agreement with the mean-field approximation in high dimensions, but not in the low dimensiond=2.
References
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Book
The P(φ)[2] Euclidean (quantum) field theory
TL;DR: Drawn primarily from the author's lectures at the Eidenossiehe Technische Hochschule, Zurich, in 1973, the volume will appeal to physicists and mathematicians alike; it is especially suitable for those with limited familiarity with the literature of this very active field.
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Infrared Bounds, Phase Transitions and Continuous Symmetry Breaking
TL;DR: In this article, it was shown that phase transitions occur in (φ·φ) 3 2 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions.
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The random-walk representation of classical spin systems and correlation inequalities
TL;DR: In this article, a unified approach to many recently established correlation inequalities was presented, and a simple proof of the mass gap for the λ(φ4)2 quantum field model was obtained.
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Proof of the Triviality of ϕ d 4 Field Theory and Some Mean-Field Features of Ising Models for d > 4
TL;DR: In this article, it is rigorously proved that the Euclidean lattice fields are free fields in the continuous limits of the Ising model, and the criticality of criticality in Ising models is defined.