Tangential Surface Pressures and Boundary Localization in Disordered Edwards--Anderson Models
Abstract
We study boundary free energies in disordered Edwards--Anderson Ising models. For rectangular strips of fixed width, we prove that the expected free-to-fixed boundary correction, divided by the tangential length, converges for every finite inverse temperature and at zero temperature. The proof combines a uniform almost-additivity estimate with product-measure concentration, yielding self-averaging along tangential intervals. We derive an exact finite-volume Gaussian interpolation identity and prove that a uniform exponential boundary-mixing condition implies boundary localization with an explicit exponential rate. The tangential pressure theorem extends to all dimensions and symmetric coupling laws with finite first moment; under a product-concentration hypothesis, self-averaging is obtained along tangential cubes. Finally, a subcritical open-bond criterion, verified explicitly for sparse signed couplings, gives low-temperature localization without assuming an infinite-volume Gibbs-state property.
Related
- Anderson localization in periodic elastic systems with random perturbations
- Localization near the edge for the lattice Anderson-Bernoulli model on general dimension
- An energy--stable ALE--FEM with compensated tangential velocity for Navier--Stokes free--boundary flows
- All-Disorder Localization for the One-Dimensional Anderson Model with Power-Law Hopping
- Perfect resonance and fragile localization suppression in correlated disordered chains
BibTeX
@misc{wang2026tangential,
title = {{Tangential Surface Pressures and Boundary Localization in Disordered Edwards--Anderson Models}},
author = {Hexiang Wang and Keheng Zhu and Mauris Chueng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20266},
eprint = {2609.20266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20266},
}
RIS
TY - UNPB
TI - Tangential Surface Pressures and Boundary Localization in Disordered Edwards--Anderson Models
AU - Hexiang Wang
AU - Keheng Zhu
AU - Mauris Chueng
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20266
UR - https://arxiv.org/abs/2609.20266
AB - We study boundary free energies in disordered Edwards--Anderson Ising models. For rectangular strips of fixed width, we prove that the expected free-to-fixed boundary correction, divided by the tangential length, converges for every finite inverse temperature and at zero temperature. The proof combines a uniform almost-additivity estimate with product-measure concentration, yielding self-averaging along tangential intervals. We derive an exact finite-volume Gaussian interpolation identity and prove that a uniform exponential boundary-mixing condition implies boundary localization with an explicit exponential rate. The tangential pressure theorem extends to all dimensions and symmetric coupling laws with finite first moment; under a product-concentration hypothesis, self-averaging is obtained along tangential cubes. Finally, a subcritical open-bond criterion, verified explicitly for sparse signed couplings, gives low-temperature localization without assuming an infinite-volume Gibbs-state property.
ER -