Home▸Physics & Mechanics▸Spin Ice Frustration: Pyrochlore Ice Rules and Magnetic Monopoles

🧊 Spin Ice Frustration: Pyrochlore Ice Rules and Magnetic Monopoles

Explore how magnetic moments on a pyrochlore lattice obey local 2-in/2-out ice rules, generating a macroscopic residual entropy and emergent monopole-like defects when the rule is broken.

Physics & Mechanics3DModerate60 FPS🔥 Fire ❄️ Ice & Cold ⚡ Plasma

The simulation shows Ising spins on a pyrochlore tetrahedral network settling into 2-in/2-out ice-rule configurations, and lets you flip a spin to watch a monopole-antimonopole pair separate along a Dirac-string trail.

🔬 What It Demonstrates

🎮 How to Use

Use the temperature slider to anneal the lattice toward the ice-rule manifold, click individual spins to flip them and create monopole defects, and toggle field direction to see the ice rule partially lift into ordered plateaus.

💡 Did You Know?

The residual entropy measured in Dy2Ti2O7 matches Linus Pauling's 1935 estimate for water ice to within a fraction of a percent, even though the underlying physics is magnetic dipoles rather than hydrogen-bonded protons.

⚙ Under the hood

Explore how magnetic moments on a pyrochlore lattice obey local 2-in/2-out ice rules, generating a macroscopic residual entropy and emergent monopole-like defects when the rule is broken.

spin icefrustrationpyrochloremagnetismentropymonopolescondensed matterstatistical physics

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install