What is Ising model: Definition and 90 Discussions

The Ising model (; German: [ˈiːzɪŋ]), named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions, as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition.The Ising model was invented by the physicist Wilhelm Lenz (1920), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model was solved by Ising (1925) himself in his 1924 thesis; it has no phase transition. The two-dimensional square-lattice Ising model is much harder and was only given an analytic description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.
In dimensions greater than four, the phase transition of the Ising model is described by mean field theory.
The Ising problem without an external field can be equivalently formulated as a graph maximum cut (Max-Cut) problem that can be solved via combinatorial optimization.

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  1. T

    I Understanding the Derivation of the Ginzburg Criterion for the Ising Model

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  2. D

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  3. C

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  4. LCSphysicist

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  5. user366312

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  6. yklee

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  7. J

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  9. W

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  10. Dom Tesilbirth

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  11. J

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  12. L

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  13. IreneFerri

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  14. J

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  16. P

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  17. J

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  18. T

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  20. T

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  22. JD_PM

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  23. G

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  25. A

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  28. Leonardo Machado

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  29. F

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  30. A

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  31. D

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  32. L

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  33. domainwhale

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  34. C

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  35. C

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  36. B

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  37. P

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  38. A

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  39. N

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  40. N

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  42. C

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  43. T

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  44. M

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  45. fluidistic

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  46. U

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  47. maajdl

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  48. A

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  49. G

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  50. W

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