| 31. | In condensed matter physics, Dyson also analysed the phase transition of the Ising model in 1 dimension and spin waves.
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| 32. | The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition.
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| 33. | When the interaction energies J _ 1, J _ 2 are both negative, the Ising model becomes an antiferromagnet.
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| 34. | For the triangular lattice, which is not bi-partite, the ferromagnetic and antiferromagnetic Ising model behave notably differently.
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| 35. | The 2-dimensional Ising model exists on a lattice, which is a collection of squares in a chessboard pattern.
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| 36. | For example, in statistical mechanics, such as the Ising model, the sum is over pairs of nearest neighbors.
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| 37. | Two such cluster models are the Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.
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| 38. | Through a mapping to the random bond Ising model, this critical probability has been found to be around 11 %.
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| 39. | The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by.
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| 40. | For the Ising model case, the equilibrium magnetization \ Psi assumes the following value below the critical temperature T _ c:
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