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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19176 |
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Table of Contents:
- We study the lattice Yang-Mills-Higgs model with inverse gauge coupling $β>0$ and Higgs length $α>0$, in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2$ and (abelian) gauge group U(1), we prove that for any $m>0$, if $α= mβ$ and $β$ is large enough, the model exhibits exponential decay of correlations. This extends the classical result of Osterwalder and Seiler (1978), who required in addition that $m$ be sufficiently large. Our result also verifies a phase diagram from the physics literature, predicted by Fradkin and Shenker (1979). The proof is based on the Glimm-Jaffe-Spencer cluster expansion around a massive Gaussian field, following the approach of Balaban et al. (1984).