  While the Ising model remains essential to understand physical phenomena, its
natural connection to combinatorial reasoning makes it also one of the best
models to probe complex systems in science and engineering. We bring a
computational lens to the study of Ising models, where our computer-science
perspective is two-fold: On the one hand, we consider the computational
complexity of the Ising partition-function problem, or #Ising, and relate it to
the logic-based counting of constraint-satisfaction problems, or #CSP. We show
that known dichotomy results for #CSP give an easy proof of the hardness of
#Ising and provide new intuition on where the difficulty of #Ising comes from.
On the other hand, we also show that #Ising can be reduced to Weighted Model
Counting (WMC). This enables us to take off-the-shelf model counters and apply
them to #Ising. We show that this WMC approach outperforms state-of-the-art
specialized tools for #Ising, thereby expanding the range of solvable problems
in computational physics.

Computational Physics;Statistical Mechanics