Decay of correlations for slowly decreasing potentials

Rigorous melts are obtained for the two-point correlations in lattice spin-/sup 1///sub 2/ systems in v-dimensional space for interaction potentials r/sup -s/ (s>0). The ferromagnetic condition is imposed. It is shown that the correlations cannot decay faster than the potential. At low activity or large magnetic field they decay precisely as r/sup -s/. For arbitrary non-zero magnetic fields and arbitrary reciprocal temperatures they decay at least as r/sup -k/. (15 refs).