Breakdown of the perturbative renormalization group for S >= 1 random antiferromagnetic spin chains

We investigate the application of a perturbative renormalization group (RG) method to random antiferromagnetic Heisenberg chains with arbitrary spin size. At zero temperature we observe that initial arbitrary probability distributions develop a singularity at J=0, for all values of spin S. When the RG method is extended to finite temperatures, without any additional assumptions, we find anomalous results for S >= 1. These results lead us to conclude that the perturbative scheme is not adequate to study random chains with S >= 1. Therefore a random singlet phase in its more restrictive definition is only assured for spin-1/2 chains.