Phase transitions in XY/Villain models and dual height functions persist under quenched disorder, and rough phases exist for annealed non-convex potentials like |∇h|^p with p≤2.
Free energy analyticity of the disordered xy model and debye screening in the 2d coulomb gas.arXiv preprint arXiv:2603.28734
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Uniform analyticity of local observables is proved in FK-percolation under mixing conditions, yielding analyticity of Potts/Ising magnetization in the supercritical regime and susceptibility in the subcritical regime.
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The impact of disorder and non-convex interactions on delocalisation of height functions
Phase transitions in XY/Villain models and dual height functions persist under quenched disorder, and rough phases exist for annealed non-convex potentials like |∇h|^p with p≤2.
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Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation
Uniform analyticity of local observables is proved in FK-percolation under mixing conditions, yielding analyticity of Potts/Ising magnetization in the supercritical regime and susceptibility in the subcritical regime.