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I was reading a book by Franco Strocchi, this one, and in some points the author claims that the case of $d=3+1$ of triviality of $\phi^4$ theory is now proven. As far as I can tell, we have just some evidence from lattice computations. Am I missing any relevant reference about this matter?

Qmechanic
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Jon
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1 Answers1

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Michael Aizenman and Hugo Duminil-Copin announced last year a proof that the scaling limit of lattice $\phi^4$ theory in 4d is trivial. It's been known since the 80s that the scaling limit is Gaussian up to logarithmic corrections for small coupling (work of Feldman, Magnen, Rivasseau, & Seneor). Aizenman & Duminil-Copin found a method which works without restriction on the interaction and field size.

Their preprint appeared on the arxiv in December. I don't think it's been formally published yet, but the argument isn't that hard to follow.

user1504
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