Spontaneous break-down of symmetry in the static ultra-local approximation of thegϕ 4 quantum field theory

Abstract

We study the spontaneous break-down of symmetry in the exactly solvable Euclidean static ultra-local model. We show that there exists always a suitable interval for the arbitrary constants from which the Green’s functions depend, and in correspondence a suitable valueλcof the coupling constant, such that forλ<λcthe theory admits the symmetric solution, while forλ⩾λcthe theory predicts also the possibility of the spontaneous break-down of the discrete symmetry.