The discrete Deffuant model and its alternatives is a family of stochastic spatial models for the dynamics of binary opinions on f issues. Another parameter is also incorporated that prevents interaction between two agents whenever their opinion profiles are at a Hamming distance greater than the confidence threshold θ. By numerical simulations, it was conjectured in (Adamopoulos and Scarlatos, Complexity 2012, 17, 43) that one‐dimensional models exhibit a phase transition at a critical value θ critical approximately equal to f/2. We (...) report on recent mathematical results on this problem that originates from the community of complex systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 437–439, 2016. (shrink)