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Ising model
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A lattice of spins explaining magnetism and phase transitions.
A lattice of spins ±1 with neighbour interactions is the simplest model of a magnet, showing spontaneous magnetisation below a critical temperature. Solved exactly in 1D and 2D.
Also used for neural networks and alloys.
No phase transition in 1D at T > 0.
In more detail
The Ising model is a simple model of magnetism, with spins on a lattice that interact with neighbours. It shows a phase transition between ordered and disordered states.
Real-world uses
- It models magnetic materials and phase transitions in physics.
- It inspires algorithms in optimisation and machine learning.
- Physicists use the Ising model to understand why iron becomes a magnet below a critical temperature.
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Frequently asked questions
What is the Ising model?
A lattice of spins that point up or down and prefer to align with neighbours.
Does it have a transition?
Yes, in two or more dimensions, at a critical temperature.
What is a spin in the Ising model?
A simple two-state variable representing a magnetic moment that points up or down on a lattice site.
Related topics in Kinetic Theory & Statistical Physics
Heat conduction at microscopic level · Transport phenomena · Phase transitions · Critical phenomena