{
  "id": "2103.11498",
  "version": "v1",
  "published": "2021-03-21T22:07:37.000Z",
  "updated": "2021-03-21T22:07:37.000Z",
  "title": "Spinodal-assisted nucleation in the two-dimensional $q-$state Potts model with short-to-long range interactions",
  "authors": [
    "Giuseppe Gagliardi",
    "Francesco Macheda"
  ],
  "comment": "20 pages, 21 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study homogeneous nucleation in the two-dimensional $q-$state Potts model for $q=3,5,10,20$ and ferromagnetic couplings $J_{ij} \\propto \\Theta (R - |i-j|)$, by means of Monte Carlo simulations employing heat bath dynamics. Metastability is induced in the low temperature phase through an instantaneous quench of the magnetic field coupled to one of the $q$ spin states. The quench depth is adjusted, depending on the value of temperature $T$, interaction range $R$, and number of states $q$, in such a way that a constant nucleation time is always obtained. In this setup we analyze the crossover between the classical compact droplet regime occurring in presence of short range interactions $R \\sim 1$, and the long-range regime $R\\gg 1$ where the properties of nucleation are influenced by the presence of a mean-field spinodal singularity. We evaluate the metastable susceptibility of the order parameter as well as various critical droplet properties, which along with the evolution of the quench depth as a function of $q,T$ and $R$, are then compared with the field theoretical predictions valid in the large $R$ limit in order to find the onset of spinodal-assisted nucleation. We find that, with a mild dependence on the values of $q$ and $T$ considered, spinodal scaling holds for interaction ranges $R\\gtrsim 8-10$, and that signatures of the presence of a pseudo-spinodal are already visible for remarkably small interaction ranges $R\\sim 4-5$. The influence of spinodal singularities on the occurrence of multi-step nucleation is also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-21T22:07:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "state potts model",
      "short-to-long range interactions",
      "spinodal-assisted nucleation",
      "simulations employing heat bath",
      "carlo simulations employing heat"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}