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Ising - The Ising Model of Ferromagnetism by Lukasz...

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The Ising Model of Ferromagnetism by Lukasz Koscielski Chem 444 Fall 2006
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Ferromagnetism Magnetic domains of a material all line up in one direction In general, domains do not line up no macroscopic magnetization Can be forced to line up in one direction Lowest energy configuration, at low T all spins aligned 2 configurations (up and down) Curie temp - temp at which ferromagnetism disappears Iron: 1043 K Critical point 2nd order phase transition
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Models Universality Class – large class of systems whose properties are independent of the dynamic details of the system Ising Model – vectors point UP OR DOWN ONLY simplest Potts Model – vectors point in any direction IN A PLANE Heisenberg Model – vectors point in any direction IN SPACE - binary alloys - binary liquid mixtures - gas-liquid (atoms and vacancies) different dimensionality different universality class - superfluid helium - superconducting metals
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Ising Model 1-D 2-D 3-D Low T High T As T increases, S increases but net magnetization decreases Solved Ising – 1925 Onsager – 1944 Proven computationally intractable - 2000
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