Proof of the Triviality ofϕd4Field Theory and Some Mean-Field Features of Ising Models ford>4

1981/07/06 by Michael Aizenman · 7 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Euclidean geometry #Geometry #Ising model #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Statistical physics #Theoretical and Computational Physics #Triviality

paper · doi:10.1103/physrevlett.47.1

openalex publication_date 1981/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04

Abstract

It is rigorously proved that the continuum limits of Euclidean \ensuremathφ_d⁴ 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.

Citations

• Infrared bounds, phase transitions and continuous symmetry breaking
• The (φ4)2 field theory as a classical Ising model

Cited by

• Semi-analytical solution of the ø4 theory on an F4 lattice
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• On decoherence in quantum gravity
• Dynamical mean-field theory for quantum spin systems: Test of solutions for magnetically ordered states
• Mode dependent field renormalization and triviality
• Scalar field theory [wikipedia]