{
  "id": "2411.04537",
  "version": "v1",
  "published": "2024-11-07T08:52:46.000Z",
  "updated": "2024-11-07T08:52:46.000Z",
  "title": "The tricritical point of tricritical directed percolation is determined based on neural network",
  "authors": [
    "Feng Gao",
    "Jianmin Shen",
    "Shanshan Wang",
    "Wei Li",
    "Dian Xu"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In recent years, neural networks have increasingly been employed to identify critical points of phase transitions. For the tricritical directed percolation model, its steady-state configurations encompass both first-order and second-order phase transitions. Due to the presence of crossover effects, identifying the critical points of phase transitions becomes challenging. This study utilizes Monte Carlo simulations to obtain steady-state configurations under different probabilities $p$ and $q$, and by calculating the increments in average particle density, we observe first-order transitions, second-order transitions, and regions where both types of transitions interact.These Monte Carlo-generated steady-state configurations are used as input to construct and train a convolutional neural network, from which we determine the critical points $p_{c}$ for different probabilities $q$. Furthermore, by learning the steady-state configurations associated with the superheated point $p=p_u$, we locate the tricritical point at $q_{t}=0.893$. Simultaneously, we employed a three-output CNN model to obtain the phase transition boundaries and the range of the crossover regions. Our method offers a neural network-based approach to capture critical points and distinguish phase transition boundaries, providing a novel solution to this problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-07T08:52:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tricritical directed percolation",
      "neural network",
      "tricritical point",
      "steady-state configurations",
      "critical points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}