Proof of the Triviality of ϕ<SUB>d</SUB><SUP>4</SUP> Field Theory and Some Mean-Field Features of Ising Models for d&gt;4

doi:10.1103/PhysRevLett.47.1

Proof of the Triviality of ϕ_d⁴ Field Theory and Some Mean-Field Features of Ising Models for d>4

Aizenman, Michael

It is rigorously proved that the continuum limits of Euclidean ϕ⁴_d 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.

Publication:

Physical Review Letters

Pub Date:

July 1981

DOI:

10.1103/PhysRevLett.47.1

Bibcode:

1981PhRvL..47....1A

Keywords:

03.50.-z;
05.50.+q;
11.10.-z;
Classical field theories;
Lattice theory and statistics;
Field theory

NASA/ADS

Proof of the Triviality of ϕd4 Field Theory and Some Mean-Field Features of Ising Models for d>4

Abstract

Proof of the Triviality of ϕ_d⁴ Field Theory and Some Mean-Field Features of Ising Models for d>4