{
  "id": "2410.23615",
  "version": "v1",
  "published": "2024-10-31T03:56:31.000Z",
  "updated": "2024-10-31T03:56:31.000Z",
  "title": "Solving the Kinetic Ising Model with Non-Reciprocity",
  "authors": [
    "Gabriel Weiderpass",
    "Mayur Sharma",
    "Savdeep Sethi"
  ],
  "comment": "72 pages, LaTeX, 13 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "hep-th",
    "nlin.SI"
  ],
  "abstract": "Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for infinite, semi-infinite and finite systems with either periodic or open boundary conditions. The exact solution allows us to explore a range of novel phenomena tied to non-reciprocity like non-reciprocity induced frustration and wave phenomena with interesting parity-dependence for finite systems of size $N$. We study dynamical questions like the approach to equilibrium with various boundary conditions. We find new regimes, separated by $N^{th}$-order exceptional points, which can be classified as overdamped, underdamped and critically damped phases. Despite these new regimes, long-time order is only present at zero temperature. Additionally, we explore the low-energy behavior of the system in various limits, including the ageing and spatio-temporal Porod regimes, demonstrating that non-reciprocity induces unique scaling behavior at zero temperature. Lastly, we present general results for systems where spins interact with no more than two spins, outlining the conditions under which long-time order may exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-31T03:56:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kinetic ising model",
      "non-reciprocity induces unique scaling behavior",
      "finite systems",
      "zero temperature",
      "long-time order"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}