# 伊辛模型可视化

统计力学中的相变与临界现象 - 交互式蒙特卡洛模拟

> 标准页面: https://elysiatools.com/zh/visualizations/ising-model

- **分类:** Physics

## 概述

Interactive visualization of the 2D Ising Model - explore phase transitions, critical phenomena, and Monte Carlo simulations in statistical mechanics. Features real-time Metropolis-Hastings algorithm simulation on N×N spin lattice (N=20-100 adjustable), temperature control from 0.1 to 6.0 with critical temperature Tc ≈ 2.269 highlighted, external magnetic field h (-2 to +2), coupling constant J (-1 to +1 for ferromagnetic/antiferromagnetic), four initial states (random, all up, all down, striped), and simulation speed control (1-100 MC steps/frame). Real-time statistics display: temperature T, T/Tc ratio, total energy E per spin, magnetization |M|, and Monte Carlo steps count. Dual chart visualization: Energy evolution and Magnetization evolution with rolling history (200 data points). Visualization options: cluster highlighting for same-spin connected regions, grid overlay toggle, and color schemes (red/blue or classic black/white). Comprehensive educational content: Ising model theory with Hamiltonian H = -J Σ⟨ij⟩ sᵢsⱼ - h Σᵢ sᵢ, historical milestones (Lenz 1920, Ising 1925, Onsager 1944), phase transition phenomena with three regimes (TTc paramagnetic disordered phase), Metropolis-Hastings algorithm steps with acceptance probability P(accept) = min(1, exp(-ΔE/kT)), observation guide for exploring low-T ferromagnetism, critical fluctuations, high-T paramagnetism, external field effects, and antiferromagnetic phase (J<0), and interactive formula breakdown explaining energy, interaction, and field terms. Observe spontaneous emergence of order from disorder, critical opalescence-like fluctuations, and the beauty of statistical mechanics. Multi-language support (zh, en, es, fr, de, ru, pt).

## 相关内容

- [零级反应 - Zero-Order Reaction](https://elysiatools.com/zh/visualizations/zero-order-reaction): 零级反应动力学和浓度随时间变化的交互式可视化
- [一级反应 - First-Order Reaction](https://elysiatools.com/zh/visualizations/first-order-reaction): 一级反应动力学和指数浓度衰减的交互式可视化
- [二级反应 - Second-Order Reaction](https://elysiatools.com/zh/visualizations/second-order-reaction): 二级反应动力学和双分子碰撞动力学的交互式可视化
- [阿伦尼乌斯方程 - Arrhenius Equation](https://elysiatools.com/zh/visualizations/arrhenius-equation): 温度对反应速率影响的交互式可视化 - 探索活化能、指数因子和速率常数的关系
- [可逆反应 - Reversible Reaction](https://elysiatools.com/zh/visualizations/reversible-reaction): A ⇌ B 可逆反应动力学的交互式可视化 - 探索正逆反应速率、平衡常数和浓度随时间的变化
- [连续反应 - Consecutive Reaction](https://elysiatools.com/zh/visualizations/consecutive-reaction): A → B → C 连续反应动力学的交互式可视化 - 探索中间物浓度峰值、决速步和所有物种的完整演化
- [链式反应 - Chain Reaction](https://elysiatools.com/zh/visualizations/chain-reaction): 自由基链式反应聚合的交互式可视化 - 探索引发、增长、终止步骤，链增长动画和分子量分布
- [勒夏特列原理 - Le Chatelier's Principle](https://elysiatools.com/zh/visualizations/le-chateliers-principle): 勒夏特列原理的交互式可视化 - 探索浓度、压强和温度变化如何影响化学平衡，配合分子动力学动画展示平衡移动过程