A remark on gauge symmetries in Ising spin glasses

This paper studies a particular line in the parameter space of the FK rando m interaction random cluster model for spin glasses following Katsura ([K]) and Mazza ([M]). We show that, after averaging over the random couplings, the occupied FK bonds have exactly a Bernoulli distribution. Comparison wit h explicit calculations on trees confirms the marginal role of FK percolati on in determining phase transitions.