  The correlation length plays a pivotal role in finite-size scaling and
hyperscaling at continuous phase transitions. Below the upper critical
dimension, where the correlation length is proportional to the system length,
both finite-size scaling and hyperscaling take conventional forms. Above the
upper critical dimension these forms break down and a new scaling scenario
appears. Here we investigate this scaling behaviour in one-dimensional Ising
ferromagnets with long-range interactions. We show that the correlation length
scales as a non-trivial power of the linear system size and investigate the
scaling forms. For interactions of sufficiently long range, the disparity
between the correlation length and the system length can be made arbitrarily
large, while maintaining the new scaling scenarios. We also investigate the
behavior of the correlation function above the upper critical dimension and the
modifications imposed by the new scaling scenario onto the associated Fisher
relation.
