Phase transition in the 2d random Potts model in the large-q limit

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Phase transition in the two-dimensional q-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random transverse-field Ising spin chain. This is supported by extensive numerical studies with a combinatorial optimization algorithm giving estimates for the critical exponents in accordance with the conjectured values: β=(3-√5)/4, βₛ=1/2 and ν=1. The specific heat has a logarithmic singularity, but at the transition point there are very strong sample-to-sample fluctuations. Discretized randomness results in discontinuities in the internal energy.