Before revision:  This result contrasts with known approximation algorithms when |\lambda|\neq 1 or b\in (\frac{\Delta-2{\Delta},}  1 ), and shows that the Lee-Yang circleof zeros is computationally intractable, even on bounded-degree graphs.
After revision:  This result contrasts with known approximation algorithms when |\lambda|\neq 1 or b\in (\frac{\Delta-2{\Delta},} 1 of the unit circle. Our work thus gives a direct connection between the presence/absence of Lee-Yang zeros and the tractability of efficiently approximating the partition function on bounded-degree graphs.