2D models of statistical physics with continuous symmetry: the case of singular interactions

Dima Ioffe, Senya Shlosman, Yvan Velenik

Published 2001-10-12Version 1

We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular interactions with continuous symmetry, when the symmetry is broken in the thermodynamic limit.