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The Ising model is a fundamental model in statistical mechanics (8.Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction, Cambridge University Press, Cambridge). Given a graph G = (V, E) with the vertex set V and edge set E, the spin Ising model is defined by choosing a spin configuration \(\omega \in \{ - {1},{1}\}^{{\text{V}}}\) via the probability \(\pi (\omega ) \propto e^{{\beta \sum_{ij \in E} \omega_{i} \omega_{j} }} ,\) with the inverse temperature β > 0.

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Finite-Size Scaling of the High-Dimensional Ising Model in Geometric Representations

  • 章节

  • 发表日期：

    2025年

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  • Tianning Xiao,
  • Zhiyi Li,
  • Sheng Fang,
  • Zongzheng Zhou,
  • Youjin Deng

摘要

The Ising model is a fundamental model in statistical mechanics (8.Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction, Cambridge University Press, Cambridge). Given a graph G = (V, E) with the vertex set V and edge set E, the spin Ising model is defined by choosing a spin configuration \(\omega \in \{ - {1},{1}\}^{{\text{V}}}\) via the probability \(\pi (\omega ) \propto e^{{\beta \sum_{ij \in E} \omega_{i} \omega_{j} }} ,\) with the inverse temperature β > 0.