A variational real-space renormalisation-group transformation based on the cumulant expansion

The first order cumulant expansion of Niemeijer and van Leeuwen (1974) is combined with a variational method to find the 'best' value of a fixed point Hamiltonian depending upon a parameter, p. A new method for calculating eigen values near this fixed point is proposed, based upon the neglect of terms proportional to the error neglected at the fixed point. This approach determines delta p/ delta K unambiguously. Calculations are carried out for a few simple models. The results are more accurate than those of most other comparably simple approaches.