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gross_neveu_model [2021/04/28 11:17]
Scott Lawrence [Gross-Neveu model] 		gross_neveu_model [2021/08/11 17:33] (current)
Scott Lawrence
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 The Gross-Neveu model is a theory of $N$ interacting fermions defined by the Lagrangian density The Gross-Neveu model is a theory of $N$ interacting fermions defined by the Lagrangian density
 \[ \[
-L = \bar\psi i \cancel{\partial} \psi + \frac{g^2}{2N} (\bar\psi \psi)^2+\mathcal L = \bar\psi i \gamma^\mu \partial_\mu \psi + \frac{g^2}{2N} (\bar\psi \psi)^2
 \text. \text.
 \] \]
  
 This model is usually studied in two dimensions, where it is asymptotically free for any $N$. However, for $2 < d < 4$, the theory is asymptotically safe: [[https://arxiv.org/pdf/1011.1456.pdf]]. Thus, there's a nontrivial CFT corresponding to the UV fixed point. This page is about that CFT. This model is usually studied in two dimensions, where it is asymptotically free for any $N$. However, for $2 < d < 4$, the theory is asymptotically safe: [[https://arxiv.org/pdf/1011.1456.pdf]]. Thus, there's a nontrivial CFT corresponding to the UV fixed point. This page is about that CFT.
 +
 +===== Large-N Limit =====
 +
 +[[https://www.sciencedirect.com/science/article/pii/037026939291265B?via%3Dihub]]
  
 ===== Other dimensions ===== ===== Other dimensions =====
  
-It is more common to study the Gross-Neveu model in two dimensions, where it is asymptotically free (so that the fixed point coincides with the theory of one free fermion field).+It is more common to study the Gross-Neveu model in two dimensions, where it is asymptotically free (so that the fixed point coincides with the theory of $N$ free fermion fields).
  
 In four dimensions this model is trivial. In four dimensions this model is trivial.
 +
 +===== See also =====
 +
 +[[gross_neveu_yukawa_model]]
  
 ===== External links ===== ===== External links =====
  
-  * [[https://en.wikipedia.org/wiki/Gross%E2%80%93Neveu_model|Wikipedia]]+  * [[https://en.wikipedia.org/wiki/Gross%E2%80%93Neveu_model|Wikipedia]] only talks about the 2d model.
Last modified: 2021/04/28 11:17
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