  We apply a new coordinate space method for the evaluation of lattice Feynman
diagrams suggested by L\"uscher and Weisz to field theories in two dimensions.
Our work is to be presented for the theories with massless propagators. The
main idea is to deal with the integrals in position space by making use of the
recursion relation for the free propagator $G(x)$ which allows to compute the
propagator recursively by its values around origin. It turns out that the
method is very efficient and gives very precise results. We illustrate the
technique by evaluating a number of two- and three-loop diagrams explicitly.
