We show that typical Renyi’s statistical mechanics’ quantifiers exhibit poles. We are referring to the partition function Z and the mean energy < U >. Renyi’s entropy is characterized by a real parameter α. The poles emerge in a numerable set of rational numbers belonging to the α-line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones. In particular, negative specific heats.Facultad de Ciencias ExactasInstituto de Física La Plata