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MENTAL MODEL · M5612

Ising Model

Ising Model
SystemsHigh supportComplexity Science
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

A simplified model describing the interaction of atomic spins in magnetic materials, used to study phase transitions and collective behavior. Near the critical temperature, the system exhibits long-range order.

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A mathematical model of collective behavior. The Ising model helps understand how simple interactions between individuals produce complex collective phenomena. In social systems, it can be used to study collective behaviors such as opinion formation and market trends.

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Each spin on a lattice takes ±1, neighboring spins interact through coupling energy J, and an external field h acts; the system energy depends on the configuration, and temperature T determines fluctuations. At low temperatures, the system tends to order (ferromagnetic), at high temperatures it becomes disordered, and a phase transition occurs at the critical temperature.

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Ising_modelZH · Explicit
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