  It is argued that self-duality of one system leads to the zero finite-size
scaling amplitude of the critical internal energy for all system belonging to
the same universality class. For such models, we may expect that condition of
equality (up to correction-to-scaling terms) of the internal energies for
systems with different sizes will yield more accurate estimates for the
critical temperature than the scaling equation for the inverse correlation
lengths which is used in the standard phenomenological renormalization-group
approach. Analytical and numerical evidences confirming the above conjecture
are given for examples of two-dimensional next-nearest-neighbour and spin-1
Ising lattices.
