Universality and the renormalisation group

Several functional renormalisation group (RG) equations including Polchinskiflows and Exact RG flows are compared from a conceptual point of view and ingiven truncations. Similarities and differences are highlighted with specialemphasis on stability properties. The main observations are worked out at theexample of O(N) symmetric scalar field theories where the flows, universalcritical exponents and scaling potentials are compared within a derivativeexpansion. To leading order, it is established that Polchinski flows and ERGflows - despite their inequivalent derivative expansions - have identicaluniversal content, if the ERG flow is amended by an adequate optimisation. Theresults are also evaluated in the light of stability and minimum sensitivityconsiderations. Extensions to higher order and further implications areemphasized.Comment: 15 pages, 2 figures; paragraph after (19), figure 2, and references adde