Variational Free Energy for a 2-Spin System
Published 2020-11-13
This was inspired by reading David MacKay's book: Information Theory, Inference, and Learning Algorithms. In Chapter 33 he explained how to compute the variational free energy of a spin system. This animation shows a two-spin system with varying inverse temperature (beta) and varying magnetization (hx, hy), the direction of which runs in a circle while the inverse temperature is changed after each round. One can see that the relative contribution of the coupling terms in the energy surface become dominant when the inverse temperature beta is raised, that is, when the temperature is lowered, and with it the contribution of the entropy part: F = E - T S.
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