Ising model

physics

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June 29, 2026

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The Ising model is a mathematical model used in statistical mechanics and has applications in physics, biology, and chemistry. It describes how the properties of individual particles are influenced by their neighbors. For instance, in a ferromagnetic material, the alignment of an atom's magnetic moment with those of its neighbors contributes to the material's overall magnetization.1

The model is particularly relevant in understanding phenomena like magnetism. In magnetic materials, electrons have magnetic moments. When these moments align in the same direction, they create a magnet. The Ising model helps explain how these individual atomic magnetic moments interact and align to produce macroscopic magnetic properties. Russian mathematician Stanislav Smirnov received the Fields Medal for his work on the Ising model, specifically proving its conformal invariance in the scaling limit for two-dimensional lattices.21

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Stanislav Smirnov
…percolation processes and on the Ising model. In percolation, a fluid flows through the spaces in a porous solid. If a material is modeled as a lattice where points have a probability for being open and allowing liquid to flow through, there is a critical probability at which a liquid…
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…percolation processes and on the Ising model. In percolation, a fluid flows through the spaces in a porous solid. If a material is modeled as a lattice where points have a probability for being open and allowing liquid to flow through, there is a critical probability at which a liquid…
Read More