# Lagrangian formulation of the Ising model as a conformal field theory

An important example of conformal field theory is the 2d Ising model, more precisely its scaling limit when the size of the lattice goes to zero. I am not an expert in the field, but this is the only description of this specific field theory I have seen in the literature.

Question. Can the above conformal field theory be described by a conformally invariant Lagrangian?

Any feedback, ideally a reference, will be helpful.

• here is one reference -- I guess there are many others. – Carlo Beenakker Dec 23 '16 at 9:17
• @CarloBeenakker: Thank you. It seems that they just claim that this is the theory of free massless Majorana fermions $(\psi,\bar \psi)$. If my understanding is correct then this answers my question. That simple... – orbits Dec 23 '16 at 9:22
• Another Lagrangian description is the bosonic $\phi^4$ model. The keywords for web search on this are "Ginzburg-Landau" formulation of CFTs. – Abdelmalek Abdesselam Dec 23 '16 at 15:30
• ...The original reference is the article "Conformal symmetry and multicritical points in two-dimensional quantum field theory" by Zamolodchikov. You can find it in books.google.com/books?id=xHHFCwAAQBAJ. – Abdelmalek Abdesselam Dec 23 '16 at 15:38