Abstract
Here we illustrate spin fluctuation theory in the example of the Ising model, where spins are treated classically and the free energy has a simple analytic form. In spin fluctuation theory, we replace the pair interaction by the interaction of spins with a fluctuating exchange field.
Theories come and go, but examples stay forever. (I.M. Gelfand)
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Notes
- 1.
Similar results in the Heisenberg model require additional approximations in the functional integral method [5].
- 2.
Here, the Fourier coefficients J q are real. They can all be made positive by shifting energy of the system (7.2) by a constant amount, which is proportional to ∑ q | S q |2.
- 3.
For magnets with itinerant electrons, see [11].
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Melnikov, N.B., Reser, B.I. (2018). Spin Fluctuation Theory in the Ising Model. In: Dynamic Spin-Fluctuation Theory of Metallic Magnetism. Springer, Cham. https://doi.org/10.1007/978-3-319-92974-3_7
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DOI: https://doi.org/10.1007/978-3-319-92974-3_7
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