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The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written: $$ H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 +\sum_{j,k,l}g_{k,l}(\mathbf{\phi}^2)^k\phi_j\Delta^l \phi_j\right] $$ In two dimensions the vector field $\phi$ is dimensionless at the gaussian fixed point, therefore I found difficult to guess which are the relevant operators and the corresponding constants $g_{k,l}$, I would like to ask if there is a simple way to estimate which operators are important to consider near the Wilson-Fischer fixed point without solving the problem.

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