SOME DIFFICULTIES ASSOCIATED WITH PARAMETER-DEPENDENT RENORMALIZATION-GROUP TRANSFORMATIONS

Certain difficulties associated with using a parameter-dependent real-space renormalization group are illustrated by a study of the one-dimensional Blume-Emery-Griffiths (BEG) model. In particular, it is noted that renormalization trajectories which are determined by optimizing the parameter-dependent free energy do not necessarily preserve the symmetries of the initial Hamiltonian and therefore can lead to incorrect results. This difficulty arises in a variational treatment of the BEG model but can be resolved by using a transformation which is the product of two successive variational renormalization transformations. © 1978 The American Physical Society.