  The two-point correlation functions of statistical models show in general
both poles and cuts in momentum space. The former correspond to the spectrum of
massive excitations of the model, while the latter originate from interaction
effects, namely creation and annihilation of virtual pairs of excitations. We
discuss the effect of such interactions on the long distance behavior of
correlation functions in configuration space, focusing on certain time-slice
operators which are commonly used to extract the spectrum. For the 3D Ising
model in the scaling region of the broken-symmetry phase, a one-loop
calculation shows that the interaction effects on time-slice correlations is
non negligible for distances up to a few times the correlation length, and
should therefore be taken into account when analysing Monte Carlo data.
