EXACT RENORMALIZATION-GROUP ANALYSIS OF 1ST-ORDER PHASE-TRANSITIONS IN CLOCK MODELS

We analyze the exact behavior of the renormalization-group flow in one -dimensional clock models that undergo first-order phase transitions b y the presence of complex interactions. The flow, defined by decimatio n, is shown to be single valued and continuous throughout its domain o f definition, which contains the transition points. This fact is in di sagreement with a recently proposed scenario for first-order phase tra nsitions claiming the existence of discontinuities of the renormalizat ion group. The results are in partial agreement with the standard scen ario. However, in the vicinity of some fixed points of the critical su rface the renormalized measure does not correspond to a renormalized H amiltonian for some choices of renormalization blocks. These pathologi es, although similar to Griffiths-Pearce pathologies, have a different physical origin: the complex character of the interactions. We elucid ate the dynamical reason for such a pathological behavior: entire regi ons of coupling constants blow up under the renormalization-group tran sformation. The flows provide nonperturbative patterns for the renorma lization-group behavior of electric conductivities in the quantum Hall effect.