The distribution of partition function zeros is studied for the ±J model
of spin glasses on the Bethe lattice. We find a relation between the
distribution of complex cavity fields and the density of zeros, which enables
us to obtain the density of zeros for the infinite system size by using the
cavity method. The phase boundaries thus derived from the location of the zeros
are consistent with the results of direct analytical calculations. This is the
first example in which the spin glass transition is related to the distribution
of zeros directly in the thermodynamical limit. We clarify how the spin glass
transition is characterized by the zeros of the partition function. It is also
shown that in the spin glass phase a continuous distribution of singularities
touches the axes of real field and temperature.Comment: 23 pages, 12 figure