{
  "abstract": "As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds $1/2$. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12862",
  "author_total": 4,
  "authors": [
    {
      "name": "Paulo H. Lorenzoni"
    },
    {
      "name": "Géza Ódor"
    },
    {
      "name": "Silvio C. Ferreira"
    },
    {
      "name": "Róbert Juhász"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ca1ctec8177k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12862",
  "fulltext_url": null,
  "id": "3ca1ctec8177k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12862",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7212549188",
  "pdf_url": "https://arxiv.org/pdf/2609.12862",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ca1ctec8177k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12862",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12862"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Slow activity decay in excitable models with discontinuous phase transitions",
  "title_text": "Slow activity decay in excitable models with discontinuous phase transitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/3ca1ctec8177k",
  "venue": "arXiv",
  "versions": []
}