At the discontinuous transition of the 2D q-Potts model for q>4, the order-order interface forms a disordered layer whose boundaries converge diffusively to a pair of non-intersecting Brownian motions.
Kadanoff and Franz J
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The Dobrushin order-disorder interface in the 2D q-Potts model for q>4 at Tc(q) converges to a Brownian bridge under diffusive scaling, with the same holding for FK-percolation.
The relative variance of the critical internal energy in the weakly disordered Baxter model approaches a finite non-zero constant as system size tends to infinity, indicating lack of self-averaging independent of the sign of g0.
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Discontinuous transition in 2D Potts: II. Order-Order Interface convergence
At the discontinuous transition of the 2D q-Potts model for q>4, the order-order interface forms a disordered layer whose boundaries converge diffusively to a pair of non-intersecting Brownian motions.
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Discontinuous transition in 2D Potts: I. Order-Disorder Interface convergence
The Dobrushin order-disorder interface in the 2D q-Potts model for q>4 at Tc(q) converges to a Brownian bridge under diffusive scaling, with the same holding for FK-percolation.
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Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model
The relative variance of the critical internal energy in the weakly disordered Baxter model approaches a finite non-zero constant as system size tends to infinity, indicating lack of self-averaging independent of the sign of g0.