  The Renormalisation Group is a versatile tool for the study of many systems
where scale-dependent behaviour is important. Its functional formulation can be
cast into the form of an exact flow equation for the scale-dependent effective
action in the presence of an infrared regularisation. The functional RG flow
for the scale-dependent effective action depends explicitly on the choice of
regulator, while the physics does not. In this work, we systematically
investigate three key aspects of how the regulator choice affects RG flows: (i)
We study flow trajectories along closed loops in the space of action
functionals varying both, the regulator scale and shape function. Such a flow
does not vanish in the presence of truncations. Based on a definition of the
length of an RG trajectory, we suggest a practical procedure for devising
optimised regularisation schemes within a truncation. (ii) In systems with
various field variables, a choice of relative cutoff scales is required. At the
example of relativistic bosonic two-field models, we study the impact of this
choice as well as its truncation dependence. We show that a crossover between
different universality classes can be induced and conclude that the relative
cutoff scale has to be chosen carefully for a reliable description of a
physical system. (iii) Non-relativistic continuum models of coupled fermionic
and bosonic fields exhibit also dependencies on relative cutoff scales and
regulator shapes. At the example of the Fermi polaron problem in three spatial
dimensions, we illustrate such dependencies and show how they can be
interpreted in physical terms.
