In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.
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Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, never within a fixed power.