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arXiv · 2608.24261

Boundary Free Energies, Quenched Mixing, and Gibbs-State Selection in Disordered Ising Models

Mauris Chueng·Hexiang Wang·Keheng Zhu
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Abstract

We study boundary free energies and half-space responses in nearest-neighbor disordered Ising models. First, we prove the existence of fixed-depth tangential pressure and identify its derivative almost everywhere with the limiting boundary response. Second, under quenched exponential boundary-response mixing, we prove Gibbs-state selection independence and exponential convergence of finite-depth pressures. We further show that uniform one-spin mixing yields DLR uniqueness and Gaussian normal localization, and verify the required mixing conditions whenever $(2d-1)\mathbb E\tanh(\beta\vert{}J\vert{})<1$. Finally, we establish an all-face surface limit in the bounded Dobrushin regime and provide counterexamples that delimit general surface and stiffness claims.

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Mauris Chueng, Hexiang Wang, Keheng Zhu. 2026-08-25. Boundary Free Energies, Quenched Mixing, and Gibbs-State Selection in Disordered Ising Models. https://arxiv.org/abs/2608.24261

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