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## Landau theory
## Additional recommended knowledgeGiven these two conditions, one can write down a phenomenological expression for the free energy as a Taylor expansion in the order parameter. For example, the Ising model free energy may be written as the following: where the parameter for physical reasons. The variable Ψ is the coarse-grained field of spins, known as the order parameter or the total magnetization. This theory of Landau first raised the order parameter to prominence. Note that the Ising model exhibits the following discrete symmetry: If every spin in the model is flipped, such that , where Landau theory has been extraordinarily useful. While the exact values of the parameters At the time, it was known experimentally that the liquid-gas coexistence curve and the ferromagnet magnetization curve both exhibited a scaling relation of the form | The extension of Landau theory to include fluctuations in the order parameter shows why Landau theory is only valid near the critical points of systems with spatial dimensions of 4 or higher. This fact is connected to the idea that Landau theory is a mean field theory. Perhaps another great drawback of Landau theory is the requirement of analyticity for the free energy; this is directly at odds with the phenomenon of phase transitions, in which one frequently observes discontinuities or divergences in derivatives of the free energy. Landau's theory for phase transitions was to provide inspiration for another theory, the Ginzburg-Landau theory of superconductivity. Categories: Statistical mechanics | Condensed matter physics |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Landau_theory". A list of authors is available in Wikipedia. |