Improved cumulant expansion for a renormalization-group treatment of Ising models

The cumulant expansion of renormalization equations proposed by Niemeijer and van Leeuwen is reexamined, resulting in a considerably improved version of the calculation of the critical properties of Ising systems. In particular the thermal and magnetic eigenvalues are determined to within 0.2 and 1.1%, respectively, of the exact values for the square lattice of spins 1/2, from the second-order calculation in this expansion.