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Proof of the Triviality of ϕ d 4 Field Theory and Some Mean-Field Features of Ising Models for d >…

1981; American Physical Society; Volume: 47; Issue: 1 Linguagem: Inglês

10.1103/physrevlett.47.1

1092-0145

Michael Aizenman,

Physics of Superconductivity and Magnetism

It is rigorously proved that the continuum limits of Euclidean ${\ensuremath{\phi}}_{d}^{4}$ lattice fields are free fields in $d>4$. An exact geometric characterization of criticality in Ising models is introduced, and used to prove other mean-field features for $d>4$ and hyperscaling in $d=2$.