{
  "abstract": "We introduce and analyze the $δ$-Ising model, a kinetic Ising ferromagnet in which single-spin flips are accepted when their energy change does not exceed a tunable threshold. Varying the field and threshold opens or closes local flip channels, dividing parameter space into kinetic sectors, each governed by a fixed Markov transition operator. We prove that the dynamics retains global spin-inversion symmetry exactly when up and down spins have equal numbers of open channels. In one such sector on a periodic chain of length $L$, unbiased random initial states therefore reach the field-aligned and antifield states with probability $1/2$ each. Closing a single channel leaves both states absorbing but makes the probability of ordering against the field decay as $(2/π)^L$. Parameter sweeps correspond to ordered products of sector operators, which separate reaching a state from holding it, so hysteresis appears when a state is reached and released at different sector boundaries. We also show how increasing the system size can induce a Mpemba-like reversal, allowing a state with more misaligned spins to reach the final ordered state sooner on average. On a periodic chain, this reversal arises because the mean absorption time grows logarithmically with system size for many short domains but linearly for a single macroscopic domain, and it disappears when the bulk flip channel is opened. These findings show how a simple, intuitive rule for Ising dynamics links local kinetic constraints to field response, memory, and relaxation within a unified framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36829",
  "author_total": 3,
  "authors": [
    {
      "name": "Dehen Cao"
    },
    {
      "name": "Wei Jiang"
    },
    {
      "name": "Ya Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3z275zk5p2meg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36829",
  "fulltext_url": null,
  "id": "3z275zk5p2meg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36829",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7224113999",
  "pdf_url": "https://arxiv.org/pdf/2610.36829",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3z275zk5p2meg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36829"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Kinetic Sectors and Nonequilibrium Dynamics in the $δ$-Ising Model",
  "title_text": "Kinetic Sectors and Nonequilibrium Dynamics in the δ-Ising Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/3z275zk5p2meg",
  "venue": "arXiv",
  "versions": []
}