In this short note, we revisit a number of classical result{s} on long-range 1D percolation, Ising model and Potts models [FS82, NS86, ACCN88, IN88]. More precisely, we show that for Bernoulli percolation, FK percolation and Potts models, there is symmetry breaking for the 1/r^2-interaction at large \beta, and that the phase transition is necessarily discontinuous. We also show, following the notation of [ACCN88] that \beta^*(q)=1 for all q\geq 1.
