  We consider m two-dimensional semi-infinite planes of Ising spins joined
together through surface spins and study the critical behaviour near to the
junction. The m=0 limit of the model - according to the replica trick -
corresponds to the semi-infinite Ising model in the presence of a random
surface field (RSFI). Using conformal mapping, second-order perturbation
expansion around the weakly- and strongly-coupled planes limits and
differential renormalization group, we show that the surface critical behaviour
of the RSFI model is described by Ising critical exponents with logarithmic
corrections to scaling, while at multiple junctions (m>2) the transition is
first order. There is a spontaneous junction magnetization at the bulk critical
point.
