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We first discuss a phenomenological mean-field theory of phase transitions due to Landau and introduce the ideas of universality and scaling near critical points. The breakdown of mean-field theory near a critical point leads us to introduce the renormalization group, which has had a major impact on our understanding of phase transitions, quantum field theory, and turbulence. We introduce the renormalization group in the context of percolation, a simple geometrical model that exhibits a continuous transition, and then apply renormalization group methods to the Ising model.
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