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.
Localization of Random Surfaces with Monotone Potentials and an FKG-Gaussian Correlation Inequality.arXiv preprint arXiv:2402.18737
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Random homomorphisms on general finite trees have root values stochastically comparable to discrete Gaussians with sub-Gaussian tails and constant-factor variance bounds controlled solely by effective resistance, extending prior results on regular trees.
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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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Random homomorphisms and Lipschitz functions on trees
Random homomorphisms on general finite trees have root values stochastically comparable to discrete Gaussians with sub-Gaussian tails and constant-factor variance bounds controlled solely by effective resistance, extending prior results on regular trees.