We consider an Ising competitive model defined over a triangular Husimi tree
where loops, responsible for an explicit frustration, are even allowed. After a
critical analysis of the phase diagram, in which a ``gas of non interacting
dimers (or spin liquid) - ferro or antiferromagnetic ordered state'' transition
is recognized in the frustrated regions, we introduce the disorder for studying
the spin glass version of the model: the triangular +/- J model. We find out
that, for any finite value of the averaged couplings, the model exhibits always
a phase transition, even in the frustrated regions, where the transition turns
out to be a glassy transition. The analysis of the random model is done by
applying a recently proposed method which allows to derive the upper phase
boundary of a random model through a mapping with a corresponding non random
one.Comment: 19 pages, 11 figures; content change
