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🧲 2D Ising Model — Metropolis Monte Carlo Ferromagnet (2D)

Interactive 2D Ising model: a square lattice of up/down spins evolved with the Metropolis Monte Carlo algorithm. Sweep temperature across the Curie point T_c ≈ 2.27 J/k_B and watch spontaneous magnetisation appear and vanish.

Physics & Mechanics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryPhysics & Mechanics

RenderingCanvas 2D

DifficultyModerate

Target FPS60

ControlsTemperature slider (Tc ≈ 2.27 J/kB marked), Coupling strength J slider, External field h slider, Lattice size slider (32² to 256²), Monte Carlo speed (sweeps per frame) slider, Pause / Play toggle, Randomize button, All Up (align) button, Periodic/fixed boundary toggle, Click or drag on the lattice to flip individual spins

ising modelmonte carlostatistical mechanicsphase transitionferromagnetismmetropolis algorithm

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⚙ Under the hood

A square lattice of up/down spins evolves under the Metropolis Monte Carlo algorithm using nearest-neighbour bonds only. Sweep the temperature across the exact Onsager critical point Tc ≈ 2.27 J/kB to watch spontaneous magnetisation appear below it and vanish into thermal disorder above it. Adjust coupling strength, external field, lattice size and boundary conditions, or flip individual spins by hand.

ising modelmonte carlostatistical mechanicsphase transitionferromagnetismmetropolis algorithm

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install