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.

<a href="https://www.compadre.org/OSP/items/detail.cfm?ID=8470">Gould, Harvey, and Jan Tobochnik. "STP Textbook Chapter 9: Critical Phenomena." In Thermal and Statistical Physics. 2009.</a>

H. Gould and J. Tobochnik, , in Thermal and Statistical Physics (2009), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8470&DocID=931).

H. Gould and J. Tobochnik, STP Textbook Chapter 9: Critical Phenomena, in Thermal and Statistical Physics (2009), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8470&DocID=931>.

Gould, H., & Tobochnik, J. (2009). STP Textbook Chapter 9: Critical Phenomena. In Thermal and Statistical Physics. Retrieved May 31, 2023, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8470&DocID=931

Gould, Harvey, and Jan Tobochnik. "STP Textbook Chapter 9: Critical Phenomena." In Thermal and Statistical Physics. 2009. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8470&DocID=931 (accessed 31 May 2023).

%0 Book Section %A Gould, Harvey %A Tobochnik, Jan %D January 12, 2009 %T STP Textbook Chapter 9: Critical Phenomena %B Thermal and Statistical Physics %8 January 12, 2009 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8470&DocID=931

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