  We present a generalized circle theorem which includes the Lee-Yang theorem
for symmetric transitions as a special case. It is found that zeros of the
partition function can be written in terms of discontinuities in the
derivatives of the free energy. For asymmetric transitions, the locus of the
zeros is tangent to the unit circle at the positive real axis in the
thermodynamic limit. For finite-size systems, they lie off the unit circle if
the partition functions of the two phases are added up with unequal prefactors.
This conclusion is substantiated by explicit calculation of zeros of the
partition function for the Blume-Capel model near and at the triple line at low
temperatures.
