Critical behavior of models with infinite disorder at a star junction of chains

We study two models having an infinite-disorder critical point-the zero temperature random transverse-field Ising model and the random contact process-on a star-like network composed of M semi-infinite chains connected to a common central site. By the strong disorder renormalization group method, the scaling dimension x(M) of the local order parameter at the junction is calculated. It is found to decrease rapidly with the number M of arms, but remains positive for any finite M. This means that, in contrast with the pure transverse-field Ising model, where the transition becomes of first order for M > 2, it remains continuous in the disordered models, although, for not too small M, it is hardly distinguishable from a discontinuous one owing to a close-to-zero x(M). The scaling behavior of the order parameter in the Griffiths-McCoy phase is also analyzed.