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We explore the possibilities of using the fermionic functionalrenormalization group to compute the phase diagram of systems with competinginstabilities. In order to overcome the ubiquituous divergences encountered inRG flows, we propose to use symmetry breaking counterterms for eachinstability, and employ a self-consistency condition for fixing thecounterterms. As a validity check, results are compared to known exact resultsfor the case of one-dimensional systems. We find that whilst one-dimensionalpeculiarities, in particular algebraically decaying correlation functions, cannot be reproduced, the phase boundaries are reproduced accurately, encouragingfurther explorations for higher-dimensional systems.

Functional renormalization group with counterterms for competing order parameters