Flowing fields and optimal RG-flows

Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate the full theory at hand, which asks for optimal expansion schemes. In the present work we use a functional renormalisation group (fRG) approach for the effective action which includes general scale-dependent reparametrisations of the theory [1]. This approach is used in an O(N)-theory to set up adaptive RG-flows that correspond to an optimal systematic expansion of the theory about the ground state or rather its full covariance or propagator. These parametrisations are induced by flowing fields that encode the differential reparametrisation steps. The approach is put to work for an investigation of the thermal phase transition in the O(4)-theory in view of applications to QCD. The respective results are compared with those obtained in standard fRG computations.