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2D Models of Statistical Physics with Continuous Symmetry: The Case of Singular Interactions D. Ioffe, S. Shlosman and Y. Velenik Commun. Math. Phys. 226, 433-454 (2002). 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. Key words: continuous symmetry, percolation, compact Lie group, recurrent random walks. Files: PDF file, Published version, bibtex