Abstract
It is shown that the isotropic Heisenberg model can be analysed in terms of a random walk on the permutation group. This approach makes it intuitively clear why the Heisenberg model exhibits long range order or ferrogmagnetic behavior in three dimensions and not in two and one dimensions. This approach to the Heisenberg model lends itself to computer analysis.
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References
MerminN.D. and WagnerH., Phys. Rev. Lett. 17, 1133 (1969).
RobinsonD.W., in Cargese Lectures in Physics, Vol. 4, (ed. by D.Kastler), Gordon and Breach, New York, 1970.
RuelleD., Statistical Mechanics, Benjamin, New York, 1969.
SpitzerF., Principles of Random Walk, Van Nostrand, Princeton, N. J., 1964.
HurstC.A. and ShermanS., Phys. Rev. Lett. 22, 1357 (1969).
Ginibre, J., in Cargese Lectures in Physics, op. cit. in [2].
BakerG.Jr., GilbertH., EveJ., and RushbrookeG., Phys. Rev. 164, 800 (1967).
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Work supported in part by the National Science Foundation
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Powers, R.T. Heisenberg model and a random walk on the permutation group. Lett Math Phys 1, 125–130 (1976). https://doi.org/10.1007/BF00398374
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DOI: https://doi.org/10.1007/BF00398374