Applicability condition of a cutoff in two-dimensional models

The paper discusses a condition of applicability for a cutoff regularization in the coordinate representation in two-dimensional Euclidean space. Several important properties and examples are presented. Specifically, it is shown that the set of functions satisfying the condition is non-empty. Furthermore, a more stringent formulation of the condition is possible. Using the example of a two-loop quantum correction for a two-dimensional non-linear sigma model, the application of the cutoff regularization is demonstrated.