A variety of Yang-Baxter maps are obtained from integrable multi-field
equations on quad-graphs. A systematic framework for investigating this
connection relies on the symmetry groups of the equations. The method is
applied to lattice equations introduced by Adler and Yamilov and which are
related to the nonlinear superposition formulae for the B\"acklund
transformations of the nonlinear Schr\"odinger system and specific
ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio