Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4 (Theorems 1.1 and 1.2)
A complete Lean 4 / Mathlib formalization of Theorems 1.1 and 1.2 of Duminil-Copin, Gagnebin, Harel, Manolescu and Tassion (arXiv:1611.09877v2). For the q-state Potts model on the square lattice with q > 4, at beta_c = log(1 + sqrt q), the q + 1 box-limit Gibbs measures are distinct and ergodic, each monochromatic measure gives its own colour probability greater than 1/q at the origin, and the inverse correlation length in the diagonal direction is lambda + 2 sum_{k >= 1} (-1)^k tanh(k lambda) / k, where cosh lambda = sqrt(q) / 2, a positive number. For the random-cluster model on the square…
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