On the DLR equation for the ( λ: φ4: + b : φ2: + μφ, μ ≠ 0) 2 euclidean quantum field theory: The uniqueness theorem

Abstract

The Dobrushin-Lanford-Ruelle (DLR) equation is studied in a certain space of measures in the case of 2-dimensional λ : φ 4: + b : φ 2: + μφ, μ ≠ 0, euclidean quantum field theory. The uniqueness theorem stating that for any μ ≠ 0 there exists unique, translationally invariant 8-regular solution of the corresponding DLR equation is proved. The theorem is proved by combining the Lee-Yang theorem with the general van Hove type theorem for infinite volume free energy densities.