Before revision:  Here, we focus on the unresolved complexity picture on the unit circle, and on the tantalising question of what happens in the circular arc around \lambda=1, where on one hand the classical algorithm of Jerrum and Sinclair gives a randomised approximation scheme on the real axis suggesting tractability, and on the other hand the presence of Lee-Yang zeros alludes to computational hardness.
After revision:  Here, we focus on the unresolved complexity picture on the unit circle, and on the tantalising question of what happens around \lambda=1, where on one hand the classical algorithm of Jerrum and Sinclair gives a randomised approximation scheme on the real axis suggesting tractability, and on the other hand the presence of Lee-Yang zeros alludes to computational hardness.