Abstract
In this chapter we will explore the critical properties of both the linear and nonlinear versions of the O(N) σ -model. By exploiting the simplifications that occur when N is large, we will show that, despite their formal differences, the two models are describing the same physics. This is an example of universality.
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Notes
For a cut-off based approach to the ϵ-expansion I recommend the article by Brézin, Le Guillou, and Zinn-Justin in volume 6 of the series Phase Transitions and Critical Phenomena, C. Domb, M. S. Green, eds. (Academic Press 1976).
The discussion of the large N limit given here closely follows that in E. Brézin, J. Zinn-Justin, Physical Review B 14 (1976) pp. 3110–3120.
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Stone, M. (2000). Large N Expansions. In: The Physics of Quantum Fields. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0507-4_18
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DOI: https://doi.org/10.1007/978-1-4612-0507-4_18
Publisher Name: Springer, New York, NY
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