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A method of exact all-order summation of leading infrared logarithms in twodimensional massless $\Phi^4$-type non-renormalizable effective field theories(EFTs) is developed. The method is applied to the ${\rm O}(N)$-symmetric EFT,which is a two-dimensional sibling of the four dimensional ${\rm O}(N+1)/{\rmO}(N)$ sigma-model. For the first time the exact all-order summation of the$\left(E^{2} \ln(1/E)\right)^n$ contributions (chiral logarithms) for the $2\to 2$ scattering amplitudes is performed in closed analytical form. The caseswhen the resulting amplitudes turn to be meromorphic functions with an infinitenumber of poles (Landau poles) are identified. This provides the first explicitexample of quasi-renormalizable field theories.

Exact summation of leading infrared logarithms in 2D effective field theories