Comments on renormalization group series

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In previous articles by Nauenberg and by Niemeijer and Ruijgrok, the renormalization group approach has been used to obtain series expansions for the free energies of certain one- dimensional spin systems. We investigate here the question of whether this method provides a fundamentally new way of approximating the largest eigenvalue of a transfer matrix or kernel. For the models mentioned above, this is not the case. The partial sums of the series are essentially equivalent to the free energies of a sequence of finite models of increasing size.