{
  "id": "2401.13299",
  "version": "v1",
  "published": "2024-01-24T08:45:26.000Z",
  "updated": "2024-01-24T08:45:26.000Z",
  "title": "Langevin dynamics of lattice Yang-Mills-Higgs and applications",
  "authors": [
    "Hao Shen",
    "Rongchan Zhu",
    "Xiangchan Zhu"
  ],
  "comment": "54 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the Langevin dynamics of various lattice formulations of the Yang-Mills-Higgs model, where the Higgs component takes values in $\\mathbb{R}^N$, $\\mathbb{S}^{N-1}$ or a Lie group. We prove the exponential ergodicity of the dynamics on the whole lattice via functional inequalities. As an application, we establish that correlations for a broad range of observables decay exponentially. Specifically, the infinite volume measure exhibits a strictly positive mass gap under strong coupling conditions. Moreover, appropriately rescaled observables exhibit factorized correlations in the large $N$ limit when the state space is compact. Our approach involves disintegration and a nuanced analysis of correlations to effectively control the unbounded Higgs component.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T08:45:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langevin dynamics",
      "lattice yang-mills-higgs",
      "application",
      "infinite volume measure",
      "correlations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}