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We then differentiate with respect to the parameter and set it equal to zero to find the minima of the Free energy. There are a few problems with this approach. First, the Free energy is not analytic in terms of the critical quantity. Second, Landau's theory does not account for the dimensionality of the system, and thus incorrectly predicts a transition in one dimension.
In order to obtain a clearer picture of transitions, physicists introduced the model of spins. The most famous of these models is the Ising model. In this model, we take a square network and put N spins on it, each with a value ? = ±1 (this value can represent either an up or down spin for an electron or a magnetic moment that points in either north or south etc...
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