Optimised Renormalisation Group Flows

We study the optimisation of exact renormalisation group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regularisation. We consider specific optimised regulators for bosonic and fermionic fields and compare the optimised ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and non-vanishing temperature. We find that optimised flows at finite temperature factorise. This corresponds to the disentangling of thermal and quantum fluctuations. A similar factorisation is found at second order in the derivative expansion. The corresponding optimised flow for a ``proper-time renormalisation group'' is also provided to leading order in the derivative expansion.