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 valueλ cof the coupling constant, such that forλ<λ cthe theory admits the symmetric solution, while forλ⩾λ cthe theory predicts also the possibility of the spontaneous break-down of the discrete symmetry.