Before revision:  We show #P-hardness for approximating the partition function on graphs of maximum degree \Delta when b, the edge-interaction parameter, is in the interval (0,\frac{\Delta-2{\Delta}} and \lambda is a non-real on the unit circle .
After revision:  We show #P-hardness for approximating the partition function on graphs of maximum degree \Delta when b, the edge-interaction parameter, is in the interval (0,\frac{\Delta-2{\Delta}} on the arc of the unit circle where the Lee-Yang zeros are dense .