INSTABILITY OF RENORMALIZATION-GROUP PATHOLOGIES UNDER DECIMATION

We investigate the stability and instability of pathologies of renorma lization group transformations for lattice spin systems under decimati on. In particular we show that, even if the original renormalization g roup transformation gives rise to a non-Gibbsian measure, Gibbsianness may be restored by applying an extra decimation transformation. This fact is illustrated in detail for the block spin transformation applie d to the Ising model. We also discuss the ease of another non-Gibbsian measure with nicely decaying correlations functions which remains non -Gibbsian after arbitrary decimation.