Top level lines in the Discrete Gaussian model converge globally to deterministic shapes with Wulff corners; macroscopic h-level lines emerge discontinuously in a window of width at most L^{1/2+o(1)}.
Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models
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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.
The paper establishes entropic repulsion of the norm and freezing of angular components in conditioned vector-valued Gaussian free fields, plus bounded norms and phase transitions for massive scalar cases.
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The limit shape and emergence of the Discrete Gaussian level lines
Top level lines in the Discrete Gaussian model converge globally to deterministic shapes with Wulff corners; macroscopic h-level lines emerge discontinuously in a window of width at most L^{1/2+o(1)}.
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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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Vector-valued Gaussian free field conditioned to avoid a ball: Entropic repulsion of the norm and Freezing of spins
The paper establishes entropic repulsion of the norm and freezing of angular components in conditioned vector-valued Gaussian free fields, plus bounded norms and phase transitions for massive scalar cases.
- A dichotomy theory for the height functions of the BKT transition